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第4行： − The term '''phase transition''' (or '''phase change''') is most commonly used to describe transitions between [[solid]], [[liquid]], and [[gas]]eous [[states of matter]], as well as [[plasma (physics)|plasma]] in rare cases. A phase of a thermodynamic system and the states of matter have uniform [[physical property|physical properties]]. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of external conditions, such as [[temperature]], [[pressure]], or others. For example, a liquid may become gas upon heating to the [[boiling point]], resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions commonly occur in nature and are used today in many technologies. − The term phase transition (or phase change) is most commonly used to describe transitions between solid, liquid, and gaseous states of matter, as well as plasma in rare cases. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of external conditions, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions commonly occur in nature and are used today in many technologies. − + − + − Examples of phase transitions include: − Examples of phase transitions include: − *The transitions between the solid, liquid, and gaseous phases of a single component, due to the effects of temperature and/or [[pressure]]: 第31行：
第26行： − {{Condensed matter physics}} − + − − + − − + − − + − − + − − + − + − + − 在以不同方式组织的'''<font color="#ff8000"> 相称commensurate</font>'''或'''<font color="#ff8000"> 不相称incommensurate</font>'''的磁性结构（如在'''<font color="#ff8000"> 锑化铈Antimonide</font>'''中）之间的转变。 + + − + − + − + − − + − 以'''<font color="#ff8000">α-钛铝化物</font>'''为例——从有序到无序的转变。 − + − 以'''<font color="#ff8000">氢</font>'''对铁（110）的依赖为例¬——吸附几何结构对覆盖率和温度存在依赖性。 − + − 当冷却到临界温度以下时，某些金属和陶瓷中出现'''<font color="#ff8000"> 超导Superconductivity</font>'''现象。 − * The transition between different molecular structures ([[Polymorphism (materials science)|polymorphs]], [[allotropy|allotropes]] or [[polyamorphism|polyamorphs]]), especially of solids, such as between an [[amorphous solid|amorphous]] structure and a [[crystal]] structure, between two different crystal structures, or between two amorphous structures. − 不同分子结构（'''<font color="#ff8000"> 同质多形体polymorphs</font>'''，'''<font color="#ff8000"> 同素异形体allotropes</font>'''或'''<font color="#ff8000"> 非晶多形体polyamorphs</font>'''）之间的转变——特别是固体之间的，例如非晶结构和晶体结构、两种不同晶体结构之间或两种非晶结构之间。 − − − − * Quantum condensation of [[boson]]ic fluids ([[Bose–Einstein condensate|Bose–Einstein condensation]]). The [[superfluidity|superfluid]] transition in liquid [[helium]] is an example of this. − '''<font color="#ff8000"> 玻色子Bosonic</font>'''流体的量子凝聚（'''<font color="#ff8000"> 玻色–爱因斯坦凝聚Bose–Einstein condensation</font>'''）。液态氦中的超流体转变就是一个例子。 − − − − * The [[Symmetry breaking|breaking of symmetries]] in the laws of physics during the early history of the universe as its temperature cooled. − 物理学中的'''<font color="#ff8000"> 对称性破裂breaking of symmetries</font>'''——发生在宇宙温度降低的早期阶段 − − − − * [[Isotope fractionation]] occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes. When [[water vapor]] condenses (an [[equilibrium fractionation]]), the heavier water isotopes (18O and 2H) become enriched in the liquid phase while the lighter isotopes (16O and 1H) tend toward the vapor phase. − '''<font color="#ff8000"> 同位素分馏Isotope fractionation</font>'''发生在相变过程中，所涉及分子的轻同位素与重同位素的比率发生变化。当水蒸气冷凝（'''<font color="#ff8000">平衡分馏equilibrium fractionation </font>）时，较重的同位素（18O和2H）在液相中富集，而较轻的同位素（16O和1H）则趋向于气相。 − − − − Phase transitions occur when the [[thermodynamic free energy]] of a system is [[analytic function|non-analytic]] for some choice of thermodynamic variables (cf. [[phase (matter)|phases]]). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. Examples include: quantum phase transitions, dynamic phase transitions, and topological (structural) phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks. − − Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables (cf. phases). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. Examples include: quantum phase transitions, dynamic phase transitions, and topological (structural) phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks. 第120行：
第83行： − At the phase transition point (for instance, [[boiling point]]) the two phases of a substance, liquid and [[vapor]], have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred. − At the phase transition point (for instance, boiling point) the two phases of a substance, liquid and vapor, have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred. 第128行：
第89行： − It is sometimes possible to change the state of a system [[diabatic]]ally (as opposed to [[adiabatic invariant|adiabatic]]ally) in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is [[metastable]], i.e., less stable than the phase to which the transition would have occurred, but not unstable either. This occurs in [[superheating]], [[supercooling]], and [[supersaturation]], for example. − It is sometimes possible to change the state of a system diabatically (as opposed to adiabatically) in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is metastable, i.e., less stable than the phase to which the transition would have occurred, but not unstable either. This occurs in superheating, supercooling, and supersaturation, for example. − + − + − [[Paul Ehrenfest]] classified phase transitions based on the behavior of the [[thermodynamic free energy]] as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. ''First-order phase transitions'' exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. ''Second-order phase transitions'' are continuous in the first derivative (the [[Phase transition#order parameters|order parameter]], which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy. These include the ferromagnetic phase transition in materials such as iron, where the [[magnetization]], which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the [[Curie temperature]]. The [[magnetic susceptibility]], the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions. − − Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. Second-order phase transitions are continuous in the first derivative (the order parameter, which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy. These include the ferromagnetic phase transition in materials such as iron, where the magnetization, which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature. The magnetic susceptibility, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions. − − The Ehrenfest classification implicitly allows for continuous phase transformations, where the bonding character of a material changes, but there is no discontinuity in any free energy derivative. An example of this occurs at the [[supercritical liquid–gas boundaries]]. − − The Ehrenfest classification implicitly allows for continuous phase transformations, where the bonding character of a material changes, but there is no discontinuity in any free energy derivative. An example of this occurs at the supercritical liquid–gas boundaries. 第154行：
第106行： − + − − In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes: − − In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes: − − − '''First-order phase transitions''' are those that involve a [[latent heat]]. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not. Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into [[water vapor|vapor]], but forms a [[turbulence|turbulent]] mixture of liquid water and vapor bubbles). [[Yoseph Imry|Imry]] and Wortis showed that [[quenched disorder]] can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling. − − First-order phase transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not. Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into vapor, but forms a turbulent mixture of liquid water and vapor bubbles). Imry and Wortis showed that quenched disorder can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling. − − − '''Second-order phase transitions''' are also called ''"continuous phase transitions"''. They are characterized by a divergent susceptibility, an infinite [[Correlation function (statistical mechanics)|correlation length]], and a [[power law]] decay of correlations near [[Critical point (thermodynamics)|criticality]]. Examples of second-order phase transitions are the [[Ferromagnetism|ferromagnetic]] transition, superconducting transition (for a [[Type-I superconductor]] the phase transition is second-order at zero external field and for a [[Type-II superconductor]] the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions) and the [[superfluid]] transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature which enables accurate detection using [[differential scanning calorimetry]] measurements. [[Lev Landau]] gave a [[Phenomenology (particle physics)|phenomenological]] [[Landau theory|theory]] of second-order phase transitions. − − Second-order phase transitions are also called "continuous phase transitions". They are characterized by a divergent susceptibility, an infinite correlation length, and a power law decay of correlations near criticality. Examples of second-order phase transitions are the ferromagnetic transition, superconducting transition (for a Type-I superconductor the phase transition is second-order at zero external field and for a Type-II superconductor the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions) and the superfluid transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature which enables accurate detection using differential scanning calorimetry measurements. Lev Landau gave a phenomenological theory of second-order phase transitions. − − − Apart from isolated, simple phase transitions, there exist transition lines as well as [[multicritical point]]s, when varying external parameters like the magnetic field or composition. − − Apart from isolated, simple phase transitions, there exist transition lines as well as multicritical points, when varying external parameters like the magnetic field or composition. − − − Several transitions are known as ''infinite-order phase transitions''.They are continuous but break no [[#Symmetry|symmetries]]. The most famous example is the [[Kosterlitz–Thouless transition]] in the two-dimensional [[XY model]]. Many [[quantum phase transition]]s, e.g., in [[two-dimensional electron gas]]es, belong to this class. − − Several transitions are known as infinite-order phase transitions.They are continuous but break no symmetries. The most famous example is the Kosterlitz–Thouless transition in the two-dimensional XY model. Many quantum phase transitions, e.g., in two-dimensional electron gases, belong to this class. 第196行：
第124行： − The [[glass transition|liquid–glass transition]] is observed in many [[polymers]] and other liquids that can be [[supercooling|supercooled]] far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a ''[[quenched disorder]]'' state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times. No direct experimental evidence supports the existence of these transitions. − The liquid–glass transition is observed in many polymers and other liquids that can be supercooled far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a quenched disorder state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times. No direct experimental evidence supports the existence of these transitions. − − The gelation transition of colloidal particles has been shown to be a second-order phase transition under nonequilibrium conditions. − + − + − A disorder-broadened first-order transition occurs over a finite range of temperatures where the fraction of the low-temperature equilibrium phase grows from zero to one (100%) as the temperature is lowered. This continuous variation of the coexisting fractions with temperature raised interesting possibilities. On cooling, some liquids vitrify into a glass rather than transform to the equilibrium crystal phase. This happens if the cooling rate is faster than a critical cooling rate, and is attributed to the molecular motions becoming so slow that the molecules cannot rearrange into the crystal positions. If the first-order freezing transition occurs over a range of temperatures, and Tg falls within this range, then there is an interesting possibility that the transition is arrested when it is partial and incomplete. Extending these ideas to first-order magnetic transitions being arrested at low temperatures, resulted in the observation of incomplete magnetic transitions, with two magnetic phases coexisting, down to the lowest temperature. First reported in the case of a ferromagnetic to anti-ferromagnetic transition, such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials,magnetocaloric materials,magnetic shape memory materials,The interesting feature of these observations of Tg falling within the temperature range over which the transition occurs is that the first-order magnetic transition is influenced by magnetic field, just like the structural transition is influenced by pressure. The relative ease with which magnetic fields can be controlled, in contrast to pressure, raises the possibility that one can study the interplay between Tg and Tc in an exhaustive way. Phase coexistence across first-order magnetic transitions will then enable the resolution of outstanding issues in understanding glasses. − A disorder-broadened first-order transition occurs over a finite range of temperatures where the fraction of the low-temperature equilibrium phase grows from zero to one (100%) as the temperature is lowered. This continuous variation of the coexisting fractions with temperature raised interesting possibilities. On cooling, some liquids vitrify into a glass rather than transform to the equilibrium crystal phase. This happens if the cooling rate is faster than a critical cooling rate, and is attributed to the molecular motions becoming so slow that the molecules cannot rearrange into the crystal positions. This slowing down happens below a glass-formation temperature Tg, which may depend on the applied pressure. If the first-order freezing transition occurs over a range of temperatures, and Tg falls within this range, then there is an interesting possibility that the transition is arrested when it is partial and incomplete. Extending these ideas to first-order magnetic transitions being arrested at low temperatures, resulted in the observation of incomplete magnetic transitions, with two magnetic phases coexisting, down to the lowest temperature. First reported in the case of a ferromagnetic to anti-ferromagnetic transition, such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials, magnetocaloric materials, magnetic shape memory materials, and other materials.The interesting feature of these observations of Tg falling within the temperature range over which the transition occurs is that the first-order magnetic transition is influenced by magnetic field, just like the structural transition is influenced by pressure. The relative ease with which magnetic fields can be controlled, in contrast to pressure, raises the possibility that one can study the interplay between Tg and Tc in an exhaustive way. Phase coexistence across first-order magnetic transitions will then enable the resolution of outstanding issues in understanding glasses. 第220行：
第142行： − + − In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the [[Critical point (thermodynamics)|critical point]], at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of [[critical opalescence]], a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light). − In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the critical point, at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of critical opalescence, a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light). 第230行：
第150行： − + − Phase transitions often involve a [[symmetry breaking]] process. For instance, the cooling of a fluid into a [[crystalline solid]] breaks continuous [[translation symmetry]]: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to [[spontaneous symmetry breaking]], with the exception of certain [[accidental symmetry|accidental symmetries]] (e.g. the formation of heavy [[virtual particles]], which only occurs at low temperatures). − Phase transitions often involve a symmetry breaking process. For instance, the cooling of a fluid into a crystalline solid breaks continuous translation symmetry: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to spontaneous symmetry breaking, with the exception of certain accidental symmetries (e.g. the formation of heavy virtual particles, which only occurs at low temperatures). 第240行：
第158行： − + − An '''order parameter''' is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other. At the critical point, the order parameter [[susceptibility (disambiguation)|susceptibility]] will usually diverge. − An order parameter is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other. At the critical point, the order parameter susceptibility will usually diverge. − − − An example of an order parameter is the net [[magnetization]] in a [[ferromagnetic]] system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities. − − An example of an order parameter is the net magnetization in a ferromagnetic system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities. − − From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the [[ferromagnetic]] phase, one must provide the net [[magnetization]], whose direction was spontaneously chosen when the system cooled below the [[Curie point]]. However, note that order parameters can also be defined for non-symmetry-breaking transitions. − − From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the ferromagnetic phase, one must provide the net magnetization, whose direction was spontaneously chosen when the system cooled below the Curie point. However, note that order parameters can also be defined for non-symmetry-breaking transitions. − − Some phase transitions, such as [[superconductivity|superconducting]] and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition. − − Some phase transitions, such as superconducting and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition. − − − There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as [[Quantum vortex|vortex]]- or [[Topological defect|defect]] lines. − − There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as vortex- or defect lines. 第282行：
第180行： − + − Symmetry-breaking phase transitions play an important role in [[physical cosmology|cosmology]]. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the [[electroweak force|electroweak field]] into the U(1) symmetry of the present-day [[electromagnetic field]]. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see [[electroweak baryogenesis]]). − Symmetry-breaking phase transitions play an important role in cosmology. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the electroweak field into the U(1) symmetry of the present-day electromagnetic field. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see electroweak baryogenesis). − − Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of [[Eric Chaisson]] and [[David Layzer]]. − − Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of Eric Chaisson and David Layzer. − − − See also [[relational order theories]] and [[order and disorder]]. − − See also relational order theories and order and disorder. 第308行：
第195行： − + − Continuous phase transitions are easier to study than first-order transitions due to the absence of [[latent heat]], and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points. − − Continuous phase transitions are easier to study than first-order transitions due to the absence of latent heat, and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points. 第318行：
第202行： − It turns out that continuous phase transitions can be characterized by parameters known as [[critical exponent]]s. The most important one is perhaps the exponent describing the divergence of the thermal [[correlation length]] by approaching the transition. For instance, let us examine the behavior of the [[heat capacity]] near such a transition. We vary the temperature {{mvar|T}} of the system while keeping all the other thermodynamic variables fixed, and find that the transition occurs at some critical temperature ''T<sub>c</sub>'' . When {{mvar|T}} is near ''T<sub>c</sub>'' , the heat capacity {{mvar|C}} typically has a [[power law]] behavior,+ − − It turns out that continuous phase transitions can be characterized by parameters known as critical exponents. The most important one is perhaps the exponent describing the divergence of the thermal correlation length by approaching the transition. For instance, let us examine the behavior of the heat capacity near such a transition. We vary the temperature of the system while keeping all the other thermodynamic variables fixed, and find that the transition occurs at some critical temperature T<sub>c</sub> . When is near T<sub>c</sub> , the heat capacity typically has a power law behavior, − − 事实证明，连续相变可以由'''<font color="#ff8000">临界指数critical exponents</font>'''这一参数表征。其中最重要的一个参数也许是描述逼近相变时热相关长度差异的指数。例如，让我们检测相变即将发生时的热容行为。在保持其他所有热力学变量不变的条件下，改变系统温度T，发现相变发生在某个临界温度Tc处。当T接近Tc时，热容C通常具有'''<font color="#ff8000">幂律行为power law behavior</font>'''： − − The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59 A similar behavior, but with the exponent {{mvar|ν}} instead of {{mvar|α}}, applies for the correlation length. − − The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59 A similar behavior, but with the exponent instead of , applies for the correlation length. − − 当接近玻璃相变温度时，非晶体材料的热容会具有幂律行为，其中通用临界指数α= 0.59。这也适用于相关长度，但要将指数改为ν。 − − The exponent {{mvar|ν}} is positive. This is different with {{mvar|α}}. Its actual value depends on the type of phase transition we are considering. − The exponent is positive. This is different with . Its actual value depends on the type of phase transition we are considering.+ − 指数ν为正数，这与α不同。临界指数的实际值取决于我们选择的相变类型。+
无编辑摘要
[[文件:Nomenclature for the different phase transitions.png|300px|thumb|right|此图显示了不同相变的命名法]]
[[文件:Nomenclature for the different phase transitions.png|300px|thumb|right|此图显示了不同相变的命名法]]
'''<font color="#ff8000"> 相变Phase transition (or phase change)</font>'''一词常用于描述物质在'''<font color="#ff8000">固态solid </font>'''，'''<font color="#ff8000">液态liquid </font>'''和'''<font color="#ff8000">气态gaseous </font>'''之间的转变，在极少数情况下还涉及'''<font color="#ff8000">等离子体plasma </font>'''。热力学系统的相和物质的状态具有统一的物理属性。由于外部条件（例如温度，压强等）的变化，在给定介质的相变过程中介质的某些属性通常会间断的发生变化。例如，液体在被加热到沸点时可能会变成气体，其体积因此发生突变。综合考量变化发生的外部条件，这种变化被称为相变。相变通常发生在自然界，如今被越来越多地用于科技行业。
'''<font color="#ff8000"> 相变Phase transition (or phase change)</font>'''一词常用于描述物质在'''<font color="#ff8000">固态solid </font>'''，'''<font color="#ff8000">液态liquid </font>'''和'''<font color="#ff8000">气态gaseous </font>'''之间的转变，在极少数情况下还涉及'''<font color="#ff8000">等离子体plasma </font>'''。热力学系统的相位和物质的状态具有统一的物理属性。由于外部条件（例如温度，压强等）的变化，在给定介质的相变过程中介质的某些属性通常会间断的发生变化。例如，液体在被加热到沸点时可能会变成气体，其体积因此发生突变。综合考量变化发生的外部条件，这种变化被称为相变。相变通常发生在自然界，如今被越来越多地用于科技行业。
== Types of phase transition 相变的种类==
==相变的种类==
[[文件:典型的相图.png|300px|thumb|right|该图为典型的相图。其中虚线部分表示了水的反常行为]]
[[文件:典型的相图.png|300px|thumb|right|该图为典型的相图。其中虚线部分表示了水的反常行为]]
相变的例子包括：
相变的例子包括：
由于温度和/或压强的影响，单组分在固相，液相和气相之间转换：
由于温度和/或压强的影响，单组分在固相，液相和气相之间转换：
[[文件:二氧化碳（红色）和水（蓝色）的相图比较.png|thumb|upright=2|二氧化碳（红色）和水（蓝色）的相图比较，解释了它们在1个大气压下的不同相变]]
[[文件:二氧化碳（红色）和水（蓝色）的相图比较.png|thumb|upright=2|二氧化碳（红色）和水（蓝色）的相图比较，解释了它们在1个大气压下的不同相变]]
* A [[eutectic]] transformation, in which a two-component single-phase liquid is cooled and transforms into two solid phases. The same process, but beginning with a solid instead of a liquid is called a [[eutectoid]] transformation.
*'''<font color="#ff8000"> 共晶转变Eutectic transformation</font>'''，即互溶液体（由两种不同成分组成的单相液体）经过冷却后转变成为两个不同的固相。如果把互溶液体改成固体，那这一过程就被称为'''<font color="#ff8000"> 共析转变 eutectoid transformation</font>'''。
'''<font color="#ff8000"> 共晶转变Eutectic transformation</font>'''，即互溶液体（由两种不同成分组成的单相液体）经过冷却后转变成为两个不同的固相。如果把互溶液体改成固体，那这一过程就被称为'''<font color="#ff8000"> 共析转变 eutectoid transformation</font>'''。
* A [[metastable]] to equilibrium phase transformation. A metastable polymorph which forms rapidly due to lower surface energy will transform to an equilibrium phase given sufficient thermal input to overcome an energetic barrier.
*亚稳态到平衡态的相变。由于较低的表面能而迅速形成的'''<font color="#ff8000"> 亚稳多晶体metastable polymorph</font>'''，在有足以克服能量位垒的热输入时会逐渐转换为一种平衡相。
亚稳态到平衡态的相变。由于较低的表面能而迅速形成的'''<font color="#ff8000"> 亚稳多晶体metastable polymorph</font>'''，在有足以克服能量位垒的热输入时会逐渐转换为一种平衡相。
* A [[peritectic]] transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase.
*'''<font color="#ff8000"> 包晶转变Peritectic transformation</font>'''。包含两种不同成分的单相固体经过加热后转变为一种固相和一种液相。
'''<font color="#ff8000"> 包晶转变Peritectic transformation</font>'''。包含两种不同成分的单相固体经过加热后转变为一种固相和一种液相。
* A [[spinodal decomposition]], in which a single phase is cooled and separates into two different compositions of that same phase.
* '''<font color="#ff8000"> 亚稳相分解Spinodal decomposition</font>'''。一个单相经过冷却后分离为两种不同的相。
'''<font color="#ff8000"> 亚稳相分解Spinodal decomposition</font>'''。一个单相经过冷却后分离为两种不同的相。
* Transition to a [[mesophase]] between solid and liquid, such as one of the "[[liquid crystal]]" phases.
* 处于固体和液体过渡状态的'''<font color="#ff8000"> 中间相mesophase</font>'''，例如一种“'''<font color="#ff8000"> 液晶liquid crystal</font>'''”相。
处于固体和液体过渡状态的'''<font color="#ff8000"> 中间相mesophase</font>'''，例如一种“'''<font color="#ff8000"> 液晶liquid crystal</font>'''”相。
* The transition between the [[ferromagnetism|ferromagnetic]] and [[paramagnetism|paramagnetic]] phases of [[magnet]]ic materials at the [[Curie point]].
*磁性材料处于'''<font color="#ff8000"> 居里点Curie point</font>'''（居里温度）时，在'''<font color="#ff8000"> 铁磁ferromagnetism</font>'''和'''<font color="#ff8000"> 顺磁paramagnetism</font>'''相之间转变。
磁性材料处于'''<font color="#ff8000"> 居里点Curie point</font>'''（居里温度）时，在'''<font color="#ff8000"> 铁磁ferromagnetism</font>'''和'''<font color="#ff8000"> 顺磁paramagnetism</font>'''相之间转变。
* 在以不同方式组织的'''<font color="#ff8000"> 相称commensurate</font>'''或'''<font color="#ff8000"> 不相称incommensurate</font>'''的磁性结构（如在'''<font color="#ff8000"> 锑化铈Antimonide</font>'''中）之间的转变。
* The transition between differently ordered, [[ANNNI model|commensurate]] or [[commensurability (mathematics)|incommensurate]], magnetic structures, such as in cerium [[antimonide]].
* '''<font color="#ff8000"> 马氏体转变Martensitic transformation</font>'''，作为碳钢的众多相变之一，也是典型的'''<font color="#ff8000"> 位移相变displacive phase transformations</font>'''
* '''<font color="#ff8000">晶体结构crystallographic structure </font>'''的变化，例如铁在'''<font color="#ff8000"> 铁素体Ferrite</font>'''和'''<font color="#ff8000"> 奥氏体Austenite</font>'''之间的转变。
* 以'''<font color="#ff8000">α-钛铝化物</font>'''为例——从有序到无序的转变。
* The [[martensitic transformation]] which occurs as one of the many phase transformations in carbon steel and stands as a model for [[displacive phase transformations]].
* 以'''<font color="#ff8000">氢</font>'''对铁（110）的依赖为例¬——吸附几何结构对覆盖率和温度存在依赖性。
'''<font color="#ff8000"> 马氏体转变Martensitic transformation</font>'''，作为碳钢的众多相变之一，也是典型的'''<font color="#ff8000"> 位移相变displacive phase transformations</font>'''
* 当冷却到临界温度以下时，某些金属和陶瓷中出现'''<font color="#ff8000"> 超导Superconductivity</font>'''现象。
* Changes in the [[crystallographic]] structure such as between [[Allotropes of iron|ferrite]] and [[austenite]] of iron.
* 不同分子结构（'''<font color="#ff8000"> 同质多形体polymorphs</font>'''，'''<font color="#ff8000"> 同素异形体allotropes</font>'''或'''<font color="#ff8000"> 非晶多形体polyamorphs</font>'''）之间的转变——特别是固体之间的，例如非晶结构和晶体结构、两种不同晶体结构之间或两种非晶结构之间。
'''<font color="#ff8000">晶体结构crystallographic structure </font>'''的变化，例如铁在'''<font color="#ff8000"> 铁素体Ferrite</font>'''和'''<font color="#ff8000"> 奥氏体Austenite</font>'''之间的转变。
* Order-disorder transitions such as in alpha-[[titanium aluminide]]s.
* '''<font color="#ff8000"> 玻色子Bosonic</font>'''流体的量子凝聚（'''<font color="#ff8000"> 玻色–爱因斯坦凝聚Bose–Einstein condensation</font>'''）。液态氦中的超流体转变就是一个例子。
* The dependence of the [[adsorption]] geometry on coverage and temperature, such as for [[hydrogen]] on iron (110).
* 物理学中的'''<font color="#ff8000"> 对称性破裂breaking of symmetries</font>'''——发生在宇宙温度降低的早期阶段
* The emergence of [[superconductivity]] in certain metals and ceramics when cooled below a critical temperature.
*'''<font color="#ff8000"> 同位素分馏Isotope fractionation</font>'''发生在相变过程中，所涉及分子的轻同位素与重同位素的比率发生变化。当水蒸气冷凝（'''<font color="#ff8000">平衡分馏equilibrium fractionation </font>）时，较重的同位素（18O和2H）在液相中富集，而较轻的同位素（16O和1H）则趋向于气相。
当系统的热力学自由能无法对某些热力学变量进行解析时，相变就会发生。这通常是因为系统中存在大量相互作用的粒子。如果系统太小，则不会出现。值得注意的是，相变同样可以存在于参数不包括温度的非热力学系统中。例如：量子相变，动态相变和拓扑（结构）相变。在这些系统中，其他参数代替了温度（在'''<font color="#ff8000"> 渗滤网络percolating networks</font>'''中，连接概率代替温度）。
当系统的热力学自由能无法对某些热力学变量进行解析时，相变就会发生。这通常是因为系统中存在大量相互作用的粒子。如果系统太小，则不会出现。值得注意的是，相变同样可以存在于参数不包括温度的非热力学系统中。例如：量子相变，动态相变和拓扑（结构）相变。在这些系统中，其他参数代替了温度（在'''<font color="#ff8000"> 渗滤网络percolating networks</font>'''中，连接概率代替温度）。
物质的两个相（液相和气相）在相变点（如沸点）具有相同的自由能，因此它们存在的可能性相同。而当温度低于沸点时，液态在两者中更稳定；当温度高于沸点时，气态更具优势。
物质的两个相（液相和气相）在相变点（如沸点）具有相同的自由能，因此它们存在的可能性相同。而当温度低于沸点时，液态在两者中更稳定；当温度高于沸点时，气态更具优势。
有时系统状态可以通过传热方式（与绝热方式相对）改变，这使系统状态得以通过相变点而又不经历相变。此时该系统会处于亚稳态（与发生了相变的相相比，其状态没有那么稳定，但也并非不稳定）。过热、过冷以及过饱和时都会发生这种现象。
有时系统状态可以通过传热方式（与绝热方式相对）改变，这使系统状态得以通过相变点而又不经历相变。此时该系统会处于亚稳态（与发生了相变的相相比，其状态没有那么稳定，但也并非不稳定）。过热、过冷以及过饱和时都会发生这种现象。
== Classifications 分类==
== 分类==
=== Ehrenfest classification 埃伦费斯特分类法 ===
=== 埃伦费斯特分类法 ===
保罗·埃伦费斯特Paul Ehrenfest根据热力学自由能和其他热力学变量的函数关系对相变进行了分类。根据他的方法，可以按照转变时的不连续自由能最低导数标记相变。'''<font color="#ff8000">一阶相变first-order phase transitions</font>'''相对于某些热力学变量，具有自由能的一阶导数不连续性。我们将各种固/液/气的转变都归为一阶相变，因为它们都涉及到密度的不连续变化——这是自由能相对于压力的一阶导数（一阶导数的逆函数）。而'''<font color="#ff8000"> 二阶相变second-order phase transitions</font>'''在一阶导数中是连续的（有序参数，即自由能相对于外部场的一阶导数，在整个转变过程中是连续的），但在自由能的二阶导数中表现出不连续性。比如'''<font color="#ff8000">铁磁相变ferromagnetic transition </font>'''（发生在铁等材料中），其中磁化强度是自由能相对于施加磁场强度的一阶导数。随着温度降低到居里温度以下，磁化强度将从零开始持续增加。而磁化率，是自由能相对于磁场的二阶导数，它的变化是不连续的。以此类推，按照Ehrenfest的分类方法，原则上可以存在第三，第四甚至更高阶的相变。
保罗·埃伦费斯特Paul Ehrenfest根据热力学自由能和其他热力学变量的函数关系对相变进行了分类。根据他的方法，可以按照转变时的不连续自由能最低导数标记相变。'''<font color="#ff8000">一阶相变first-order phase transitions</font>'''相对于某些热力学变量，具有自由能的一阶导数不连续性。我们将各种固/液/气的转变都归为一阶相变，因为它们都涉及到密度的不连续变化——这是自由能相对于压力的一阶导数（一阶导数的逆函数）。而'''<font color="#ff8000"> 二阶相变second-order phase transitions</font>'''在一阶导数中是连续的（有序参数，即自由能相对于外部场的一阶导数，在整个转变过程中是连续的），但在自由能的二阶导数中表现出不连续性。比如'''<font color="#ff8000">铁磁相变ferromagnetic transition </font>'''（发生在铁等材料中），其中磁化强度是自由能相对于施加磁场强度的一阶导数。随着温度降低到居里温度以下，磁化强度将从零开始持续增加。而磁化率，是自由能相对于磁场的二阶导数，它的变化是不连续的。以此类推，按照Ehrenfest的分类方法，原则上可以存在第三，第四甚至更高阶的相变。
'''<font color="#ff8000"> 埃伦费斯特分类法Ehrenfest classification</font>'''隐含连续相变，其中材料的成键特征发生了变化，但任何自由能导数都没有间断。比如说超临界液气的边界。
'''<font color="#ff8000"> 埃伦费斯特分类法Ehrenfest classification</font>'''隐含连续相变，其中材料的成键特征发生了变化，但任何自由能导数都没有间断。比如说超临界液气的边界。
=== Modern classifications 现代分类法 ===
===现代分类法 ===
在现代分类方案中，相变被分为两大类，命名方式类似于埃伦费斯特分类法：
在现代分类方案中，相变被分为两大类，命名方式类似于埃伦费斯特分类法：
一阶相变是那些涉及潜伏热的相变。在这种相变过程中，系统会吸收或释放固定（通常是大量）的能量。在此过程中，即使热量增加，系统的温度也保持恒定：系统处于“混合相状态”，也就是说某些部分已完成转变，而其他部分尚未完成。常见的例子是冰的融化或水的沸腾（水不会立即变成蒸气，而是成为液态水和蒸气气泡的湍流混合物）。物理学家伊姆利 Imry和沃迪斯 Wortis研究发现，可以将'''<font color="#ff8000"> 淬火无序quenched disorder</font>'''视为一阶转变。即在有限的温度范围内完成相变，但是过冷或过热现象仍然存在，并且滞后仍然存在于热循环中。
一阶相变是那些涉及潜伏热的相变。在这种相变过程中，系统会吸收或释放固定（通常是大量）的能量。在此过程中，即使热量增加，系统的温度也保持恒定：系统处于“混合相状态”，也就是说某些部分已完成转变，而其他部分尚未完成。常见的例子是冰的融化或水的沸腾（水不会立即变成蒸气，而是成为液态水和蒸气气泡的湍流混合物）。物理学家伊姆利 Imry和沃迪斯 Wortis研究发现，可以将'''<font color="#ff8000"> 淬火无序quenched disorder</font>'''视为一阶转变。即在有限的温度范围内完成相变，但是过冷或过热现象仍然存在，并且滞后仍然存在于热循环中。
'''<font color="#ff8000">二阶相变Second-order phase transitions </font>'''，或称为“连续相变”，它们的特征是敏感度发散，相关长度无限以及接近临界的相关性幂律衰减。二阶相变的例子是铁磁相变，'''<font color="#ff8000">超导相变superconducting transition </font>'''（对于I型超导体，在零外场下的相变是二阶的;对于II型超导体，从常态到混合态以及混合态到超导状态的转变都是二阶的）和'''<font color="#ff8000">超流体转换superfluid transition </font>'''。另外，对'''<font color="#ff8000">非晶体材料amorphous materials</font>'''而言，'''<font color="#ff8000">热膨胀thermal expansion</font>'''和'''<font color="#ff8000">热容属性heat capacity</font>'''在玻璃相变温度下会发生突变——这与粘度属性相反。我们可以使用差示扫描量热法来精确检测变化数值。列夫·兰道Lev Landau后来得出了二阶相变的现象学理论。
'''<font color="#ff8000">二阶相变Second-order phase transitions </font>'''，或称为“连续相变”，它们的特征是敏感度发散，相关长度无限以及接近临界的相关性幂律衰减。二阶相变的例子是铁磁相变，'''<font color="#ff8000">超导相变superconducting transition </font>'''（对于I型超导体，在零外场下的相变是二阶的;对于II型超导体，从常态到混合态以及混合态到超导状态的转变都是二阶的）和'''<font color="#ff8000">超流体转换superfluid transition </font>'''。另外，对'''<font color="#ff8000">非晶体材料amorphous materials</font>'''而言，'''<font color="#ff8000">热膨胀thermal expansion</font>'''和'''<font color="#ff8000">热容属性heat capacity</font>'''在玻璃相变温度下会发生突变——这与粘度属性相反。我们可以使用差示扫描量热法来精确检测变化数值。列夫·兰道Lev Landau后来得出了二阶相变的现象学理论。
当改变诸如磁场、成分之类的外部参数时，除了独立、简单的相变，还存在'''<font color="#ff8000">跃迁谱线transition lines</font>'''以及多个'''<font color="#ff8000">临界点multicritical points</font>'''。
当改变诸如磁场、成分之类的外部参数时，除了独立、简单的相变，还存在'''<font color="#ff8000">跃迁谱线transition lines</font>'''以及多个'''<font color="#ff8000">临界点multicritical points</font>'''。
另外还存在其他相变类型,例如'''<font color="#ff8000">无限阶相变 infinite-order phase transitions</font>'''。无限阶相变是连续的,但并不破坏对称性。最著名的例子是二维XY模型中的'''<font color="#ff8000">KS相变 Kosterlitz-Thouless transition</font>'''。除此之外, '''<font color="#ff8000">二维电子气two-dimensional electron gases </font>'''中的量子相变也属于无限阶相变。
另外还存在其他相变类型,例如'''<font color="#ff8000">无限阶相变 infinite-order phase transitions</font>'''。无限阶相变是连续的,但并不破坏对称性。最著名的例子是二维XY模型中的'''<font color="#ff8000">KS相变 Kosterlitz-Thouless transition</font>'''。除此之外, '''<font color="#ff8000">二维电子气two-dimensional electron gases </font>'''中的量子相变也属于无限阶相变。
在被冷却至远低于结晶相熔点的聚合物和其他液体中出现了'''<font color="#ff8000">液体-玻璃相变liquid–glass transition</font>'''。综合考虑多个方面，我们认为这是一种非典型相变。它不是热力学基态之间的转变：因为人们普遍认为，真正的基态始终是晶体。玻璃是淬火无序状态，其'''<font color="#ff8000">熵entropy</font>'''、'''<font color="#ff8000">密度density</font>'''等取决于热历史。因此，可以把玻璃相变看作一种动态现象：液体冷却时，其内部自由度会逐渐失去平衡。一些理论预测其潜在相变会发生在无限长'''<font color="#ff8000">弛豫时间relaxation times</font>'''的假设极限内。但是目前并不存在直接的实验证据来支持其存在。
在被冷却至远低于结晶相熔点的聚合物和其他液体中出现了'''<font color="#ff8000">液体-玻璃相变liquid–glass transition</font>'''。综合考虑多个方面，我们认为这是一种非典型相变。它不是热力学基态之间的转变：因为人们普遍认为，真正的基态始终是晶体。玻璃是淬火无序状态，其'''<font color="#ff8000">熵entropy</font>'''、'''<font color="#ff8000">密度density</font>'''等取决于热历史。因此，可以把玻璃相变看作一种动态现象：液体冷却时，其内部自由度会逐渐失去平衡。一些理论预测其潜在相变会发生在无限长'''<font color="#ff8000">弛豫时间relaxation times</font>'''的假设极限内。但是目前并不存在直接的实验证据来支持其存在。
在非平衡条件下，'''<font color="#ff8000">胶体粒子colloidal particles</font>'''的凝胶化转变被认为是二级相变。
在非平衡条件下，'''<font color="#ff8000">胶体粒子colloidal particles</font>'''的凝胶化转变被认为是二级相变。
== Characteristic properties 特征属性 ==
==特征属性 ==
=== Phase coexistence 相共存 ===
=== 相共存 ===
在有限的温度范围内，胶体粒子的凝胶化转变显示为bA紊乱-扩展的一阶转变。随着温度降低，'''<font color="#ff8000">低温平衡相low-temperature equilibrium phase</font>'''的分数从零增加到一（100％）。随温度变化而变化的馏分共存创造了许多有趣的可能性。比如在冷却时，一些液体会逐渐玻璃化，而不是转变为'''<font color="#ff8000">平衡晶相equilibrium crystal phase</font>'''。这种情况往往发生在冷却速率比临界冷却速率快的时候——分子运动变得十分缓慢，以至于分子无法重新排列到晶体位置。分子运动的减速通常发生在气温降至玻璃的形成温度Tg以下时——这可能需要外部施加压力来实现。如果Tg落在该一阶冻结相变发生的特定温度范围内，一种有趣的现象就会发生，即当转变不完整时该转变会停止。同理可以考虑在低温下被阻止的一阶磁相变，我们可以观察到不完全的磁相变，即两个磁相同时存在直至到达最低温度。自关于铁磁到反铁磁相变的报道首次公开以来，人们逐渐发现了各种一阶磁相变的持久相共存现象。包括'''<font color="#ff8000">庞磁电阻锰矿材料colossal-magnetoresistance manganite materials</font>'''、'''<font color="#ff8000">磁制冷材料magnetocaloric materials</font>'''、'''<font color="#ff8000">磁性形状记忆材料magnetic shape memory materials</font>'''等。当Tg落在相变发生的温度范围内时，观测结果非常有趣，其一阶磁相变受到了磁场的影响——就像结构相变会受到压力影响一样。不过与压力相比，控制磁场相对容易，这大大提高了研究者们运用穷举法研究Tg和Tc之间相互作用的成功率。一阶磁相变的相位共存将有助于解决和玻璃有关的一系列突出问题。
在有限的温度范围内，胶体粒子的凝胶化转变显示为bA紊乱-扩展的一阶转变。随着温度降低，'''<font color="#ff8000">低温平衡相low-temperature equilibrium phase</font>'''的分数从零增加到一（100％）。随温度变化而变化的馏分共存创造了许多有趣的可能性。比如在冷却时，一些液体会逐渐玻璃化，而不是转变为'''<font color="#ff8000">平衡晶相equilibrium crystal phase</font>'''。这种情况往往发生在冷却速率比临界冷却速率快的时候——分子运动变得十分缓慢，以至于分子无法重新排列到晶体位置。分子运动的减速通常发生在气温降至玻璃的形成温度Tg以下时——这可能需要外部施加压力来实现。如果Tg落在该一阶冻结相变发生的特定温度范围内，一种有趣的现象就会发生，即当转变不完整时该转变会停止。同理可以考虑在低温下被阻止的一阶磁相变，我们可以观察到不完全的磁相变，即两个磁相同时存在直至到达最低温度。自关于铁磁到反铁磁相变的报道首次公开以来，人们逐渐发现了各种一阶磁相变的持久相共存现象。包括'''<font color="#ff8000">庞磁电阻锰矿材料colossal-magnetoresistance manganite materials</font>'''、'''<font color="#ff8000">磁制冷材料magnetocaloric materials</font>'''、'''<font color="#ff8000">磁性形状记忆材料magnetic shape memory materials</font>'''等。当Tg落在相变发生的温度范围内时，观测结果非常有趣，其一阶磁相变受到了磁场的影响——就像结构相变会受到压力影响一样。不过与压力相比，控制磁场相对容易，这大大提高了研究者们运用穷举法研究Tg和Tc之间相互作用的成功率。一阶磁相变的相位共存将有助于解决和玻璃有关的一系列突出问题。
=== Critical points 临界点===
===临界点===
在任何包含液相和气相的系统中都存在压力和温度的特殊组合，我们称之为临界点。在该临界点处，液相和气相之间的转变即为二级相变。在临界点附近，如果流体足够热并且被压缩，那么液相和气相之间的区别几乎就消失了。这与临界乳光现象有关——液体在所有可能的波长（包括可见光）处产生密度波动，变成乳白色。
在任何包含液相和气相的系统中都存在压力和温度的特殊组合，我们称之为临界点。在该临界点处，液相和气相之间的转变即为二级相变。在临界点附近，如果流体足够热并且被压缩，那么液相和气相之间的区别几乎就消失了。这与临界乳光现象有关——液体在所有可能的波长（包括可见光）处产生密度波动，变成乳白色。
=== Symmetry 对称性===
=== 对称性===
相变通常涉及到对称破坏。例如，将流体冷却至成结晶固体会破坏其连续的平移对称性：流体中的每个点都具有相同的属性，但是晶体中的点并非如此（除非这些点来自晶格点阵中的晶格点）。通常，由于'''<font color="#ff8000"> 自发对称性破缺spontaneous symmetry breaking</font>'''，除了某些特殊的对称性（例如，'''<font color="#ff8000"> 重虚粒子Virtual particles</font>'''的形成，其仅在低温下发生）外，高温相比低温相具有更多的对称性。
相变通常涉及到对称破坏。例如，将流体冷却至成结晶固体会破坏其连续的平移对称性：流体中的每个点都具有相同的属性，但是晶体中的点并非如此（除非这些点来自晶格点阵中的晶格点）。通常，由于'''<font color="#ff8000"> 自发对称性破缺spontaneous symmetry breaking</font>'''，除了某些特殊的对称性（例如，'''<font color="#ff8000"> 重虚粒子Virtual particles</font>'''的形成，其仅在低温下发生）外，高温相比低温相具有更多的对称性。
=== Order parameters 序参数 ===
=== 序参数 ===
'''<font color="#ff8000"> 序参数Order parameter</font>'''是相变系统中跨边界的有序/无序度量；它通常在一个为零的阶段（通常在临界点以上）和一个非零阶段之间。在临界点，序参数的敏感性通常会有分离趋向。
'''<font color="#ff8000"> 序参数Order parameter</font>'''是相变系统中跨边界的有序/无序度量；它通常在一个为零的阶段（通常在临界点以上）和一个非零阶段之间。在临界点，序参数的敏感性通常会有分离趋向。
序参数的一个示例是发生相变的铁磁系统中的净磁化强度。对于液/气相而言，序参数就是它们的密度之差。
序参数的一个示例是发生相变的铁磁系统中的净磁化强度。对于液/气相而言，序参数就是它们的密度之差。
从理论的角度来看，序参数来自对称性破坏。当发生这种情况时，需要引入一个或多个他变量来描述该系统状态。例如，在铁磁相中必须提供净磁化强度，因为当系统降温至居里点以下时，磁化方向会自动确定。但是值得注意的是，非对称性破坏相变也可以定义有序参数。
从理论的角度来看，序参数来自对称性破坏。当发生这种情况时，需要引入一个或多个他变量来描述该系统状态。例如，在铁磁相中必须提供净磁化强度，因为当系统降温至居里点以下时，磁化方向会自动确定。但是值得注意的是，非对称性破坏相变也可以定义有序参数。
某些相变，例如'''<font color="#ff8000"> 超导superconducting</font>'''和铁磁，可以具有超过一个自由度的多个序参数。在这样的相中，序参数可以采用复数、'''<font color="#ff8000">向量vector</font>'''甚至'''<font color="#ff8000">张量tensor</font>'''的形式，其大小在相变发生时会变为零。
某些相变，例如'''<font color="#ff8000"> 超导superconducting</font>'''和铁磁，可以具有超过一个自由度的多个序参数。在这样的相中，序参数可以采用复数、'''<font color="#ff8000">向量vector</font>'''甚至'''<font color="#ff8000">张量tensor</font>'''的形式，其大小在相变发生时会变为零。
'''<font color="#ff8000">无序参数disorder parameters</font>'''中存在着相变的双重表述。 这就证明了'''<font color="#ff8000"> 线状激励line-like excitations</font>'''确实存在，例如'''<font color="#ff8000"> 涡旋线vortex lines</font>'''，'''<font color="#ff8000"> 缺陷线defect lines</font>'''等。
'''<font color="#ff8000">无序参数disorder parameters</font>'''中存在着相变的双重表述。 这就证明了'''<font color="#ff8000"> 线状激励line-like excitations</font>'''确实存在，例如'''<font color="#ff8000"> 涡旋线vortex lines</font>'''，'''<font color="#ff8000"> 缺陷线defect lines</font>'''等。
=== Relevance in cosmology 宇宙学的相关性 ===
===宇宙学的相关性 ===
对称性破坏相变在宇宙学中起着重要作用。随着宇宙的膨胀和冷却，太空经历了一系列对称性破坏的相变。例如，电弱过渡破坏了当时电弱场的''SU（2）×U（1）''对称性，生成了当今电磁场的''U（1）''对称性。一旦明白宇宙发生过这种转变，对当今宇宙中物质与反物质之间不对称性的研究对我们来说也就更好理解了（请参阅'''<font color="#ff8000"> 弱电重子生成electroweak baryogenesis</font>'''）。
对称性破坏相变在宇宙学中起着重要作用。随着宇宙的膨胀和冷却，太空经历了一系列对称性破坏的相变。例如，电弱过渡破坏了当时电弱场的''SU（2）×U（1）''对称性，生成了当今电磁场的''U（1）''对称性。一旦明白宇宙发生过这种转变，对当今宇宙中物质与反物质之间不对称性的研究对我们来说也就更好理解了（请参阅'''<font color="#ff8000"> 弱电重子生成electroweak baryogenesis</font>'''）。
埃里克·蔡森Eric Chaisson和戴维·莱泽David Layzer的研究表明，相变正在不断膨胀的宇宙中进行，这与宇宙秩序的发展变化有关。
埃里克·蔡森Eric Chaisson和戴维·莱泽David Layzer的研究表明，相变正在不断膨胀的宇宙中进行，这与宇宙秩序的发展变化有关。
详情另参见'''<font color="#ff8000">关系秩序理论relational order theories</font>'''和秩序与无序。
详情另参见'''<font color="#ff8000">关系秩序理论relational order theories</font>'''和秩序与无序。
=== Critical exponents and universality classes 临界指数和普适性 ===
=== 临界指数和普适性 ===
由于不存在'''<font color="#ff8000"> 潜伏热latent heat</font>'''，连续相变比一阶相变更容易研究。目前人们已经发现了许多有趣的性质。与连续相变有关的现象由于与临界点有关而被称为临界现象。
由于不存在'''<font color="#ff8000"> 潜伏热latent heat</font>'''，连续相变比一阶相变更容易研究。目前人们已经发现了许多有趣的性质。与连续相变有关的现象由于与临界点有关而被称为临界现象。
事实证明，连续相变可以由'''<font color="#ff8000">临界指数critical exponents</font>'''这一参数表征。其中最重要的一个参数也许是描述逼近相变时热相关长度差异的指数。例如，让我们检测相变即将发生时的热容行为。在保持其他所有热力学变量不变的条件下，改变系统温度T，发现相变发生在某个临界温度 ''T<sub>c</sub>''处。当{{mvar|T}}接近''T<sub>c</sub>'' 时，热容{{mvar|C}} 通常具有'''<font color="#ff8000">[[幂律]]行为power law behavior</font>'''：
<math> C \propto |T_c - T|^{-\alpha}.</math>
<math> C \propto |T_c - T|^{-\alpha}.</math>
当接近玻璃相变温度时，非晶体材料的热容会具有幂律行为，其中通用临界指数{{mvar|α}}= 0.59。这也适用于相关长度，但要将指数改为{{mvar|ν}}。
指数{{mvar|ν}}为正数，这与{{mvar|α}}不同。临界指数的实际值取决于我们选择的相变类型。