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* 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.

* 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.

共晶转变Eutectic transformation指的是一类互溶液体（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。同样的过程，由一类固态开始转变成为两个不同的固相，则称为共析转变。

'''<font color="#ff8000"> 共晶转变Eutectic transformation</font>'''指的是一类互溶液体（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。同样的过程，由一类固态开始转变成为两个不同的固相，则称为共析转变。

 

* 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.

* 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.

由于较低的表面能而迅速形成的亚稳多晶体Metastable polymorph会逐渐趋向一种平衡相，前提是需要足够的热输入以克服能量位垒。

由于较低的表面能而迅速形成的'''<font color="#ff8000"> 文字</font>'''亚稳多晶体Metastable polymorph会逐渐趋向一种平衡相，前提是需要足够的热输入以克服能量位垒。

* A [[peritectic]] transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase.

* A [[peritectic]] transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase.

包晶转变Peritectic transformation，指的是一类单相固体（包含两种不同成分）经过加热后转变为一种固相和一种液相的过程。

'''<font color="#ff8000"> 文字</font>'''包晶转变Peritectic transformation，指的是一类单相固体（包含两种不同成分）经过加热后转变为一种固相和一种液相的过程。

* A [[spinodal decomposition]], in which a single phase is cooled and separates into two different compositions of that same phase.

* A [[spinodal decomposition]], in which a single phase is cooled and separates into two different compositions of that same phase.

亚稳相分解Spinodal decomposition，指的是一个单相经过冷却后分离为同相的两种不同成分的物质。

'''<font color="#ff8000"> 文字</font>'''亚稳相分解Spinodal decomposition，指的是一个单相经过冷却后分离为同相的两种不同成分的物质。

* Transition to a [[mesophase]] between solid and liquid, such as one of the "[[liquid crystal]]" phases.

* Transition to a [[mesophase]] between solid and liquid, such as one of the "[[liquid crystal]]" phases.

在固体和液体之间过渡的中间相Mesophase，例如“液晶Liquid crystal”相之一。

在固体和液体之间过渡的'''<font color="#ff8000"> 文字</font>'''中间相Mesophase，例如“'''<font color="#ff8000"> 文字</font>'''液晶Liquid crystal”相之一。

* The transition between the [[ferromagnetism|ferromagnetic]] and [[paramagnetism|paramagnetic]] phases of [[magnet]]ic materials at the [[Curie point]].

* The transition between the [[ferromagnetism|ferromagnetic]] and [[paramagnetism|paramagnetic]] phases of [[magnet]]ic materials at the [[Curie point]].

* The transition between differently ordered, [[ANNNI model|commensurate]] or [[commensurability (mathematics)|incommensurate]], magnetic structures, such as in cerium [[antimonide]].

* The transition between differently ordered, [[ANNNI model|commensurate]] or [[commensurability (mathematics)|incommensurate]], magnetic structures, such as in cerium [[antimonide]].

* The [[martensitic transformation]] which occurs as one of the many phase transformations in carbon steel and stands as a model for [[displacive phase transformations]].

* The [[martensitic transformation]] which occurs as one of the many phase transformations in carbon steel and stands as a model for [[displacive phase transformations]].

马氏体转变Martensitic transformatio是碳钢的众多相变之一，是典型的位移相变Displacive phase transformationsD

'''<font color="#ff8000"> 文字</font>'''马氏体转变Martensitic transformatio是碳钢的众多相变之一，是典型的'''<font color="#ff8000"> 文字</font>'''位移相变Displacive phase transformationsD

* Changes in the [[crystallographic]] structure such as between [[Allotropes of iron|ferrite]] and [[austenite]] of iron.

* Changes in the [[crystallographic]] structure such as between [[Allotropes of iron|ferrite]] and [[austenite]] of iron.

* Order-disorder transitions such as in alpha-[[titanium aluminide]]s.

* Order-disorder transitions such as in alpha-[[titanium aluminide]]s.

有序到无序的转变，例如α-钛铝化物Titanium aluminide。

有序到无序的转变，例如α-钛铝化物。

* The emergence of [[superconductivity]] in certain metals and ceramics when cooled below a critical temperature.

* The emergence of [[superconductivity]] in certain metals and ceramics when cooled below a critical temperature.

* The transition between different molecular structures ([[Polymorphism (materials science)|polymorphs]], [[allotropy|allotropes]] or [[polyamorphism|polyamorphs{{not a typo}}]]), 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.

* The transition between different molecular structures ([[Polymorphism (materials science)|polymorphs]], [[allotropy|allotropes]] or [[polyamorphism|polyamorphs{{not a typo}}]]), 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.

* Quantum condensation of [[boson]]ic fluids ([[Bose–Einstein condensate|Bose–Einstein condensation]]). The [[superfluidity|superfluid]] transition in liquid [[helium]] is an example of this.

* Quantum condensation of [[boson]]ic fluids ([[Bose–Einstein condensate|Bose–Einstein condensation]]). The [[superfluidity|superfluid]] transition in liquid [[helium]] is an example of this.

玻色子Bosonic流体的量子凝聚（玻色–爱因斯坦凝聚Bose–Einstein condensation）。液态氦中的超流体转变就是一个例子。

'''<font color="#ff8000"> 文字</font>'''玻色子Bosonic流体的量子凝聚（'''<font color="#ff8000"> 文字</font>'''玻色–爱因斯坦凝聚Bose–Einstein condensation）。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.

* The [[Symmetry breaking|breaking of symmetries]] in the laws of physics during the early history of the universe as its temperature cooled.

早期的宇宙随着温度的降温，物理学定律的对称性破裂Breaking of symmetries。

早期的宇宙随着温度的降温，物理学定律的'''<font color="#ff8000"> 文字</font>'''对称性破裂Breaking of symmetries。

* [[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.

* [[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.

同位素分馏Isotope fractionation发生在相变过程中，所涉及分子中的轻同位素与重同位素的比率会发生变化。当水蒸气冷凝（平衡分馏）时，较重的水同位素（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。

'''<font color="#ff8000"> 文字</font>'''同位素分馏Isotope fractionation发生在相变过程中，所涉及分子中的轻同位素与重同位素的比率会发生变化。当水蒸气冷凝（平衡分馏）时，较重的水同位素（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 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.

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.

当一个系统的热力学自由能对于某些热力学变量（参见相）选择不解析时，就会发生相变。这种情况通常是由于系统中存在大量粒子相互作用，如果系统太小，则不太会出现。值得注意的是，相变的发生和定义同样可以针对于非热力学系统，并且不将温度作为参数。例如：量子相变，动态相变和拓扑（结构）相变。在这些类型的系统中，其他参数代替了温度。例如，连接概率代替渗滤网络Percolating networks的温度。

当一个系统的热力学自由能对于某些热力学变量（参见相）选择不解析时，就会发生相变。这种情况通常是由于系统中存在大量粒子相互作用，如果系统太小，则不太会出现。值得注意的是，相变的发生和定义同样可以针对于非热力学系统，并且不将温度作为参数。例如：量子相变，动态相变和拓扑（结构）相变。在这些类型的系统中，其他参数代替了温度。例如，连接概率代替'''<font color="#ff8000"> 文字</font>'''渗滤网络Percolating networks的温度。

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.

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.

保罗·埃伦费斯特Paul Ehrenfest根据热力学自由能与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，可以将相变按照转变时的不连续自由能的最低导数标记。一阶相变相对于某些热力学变量，表现出自由能的一阶导数不连续。各种固/液/气的转变都归为一阶相变First-order phase transitions，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）。而二阶相变Second-order phase transitions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。比如包括铁等材料中的铁磁相变，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连续增加。而磁化率，是自由能相对于磁场的二阶导数，它的变化则是不连续的。以此类推，按照埃伦费斯特的分类方法，原则上可以存在第三，第四和更高阶的相变。

保罗·埃伦费斯特Paul Ehrenfest根据热力学自由能与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，可以将相变按照转变时的不连续自由能的最低导数标记。一阶相变相对于某些热力学变量，表现出自由能的一阶导数不连续。各种固/液/气的转变都归为'''<font color="#ff8000"> 文字</font>'''一阶相变First-order phase transitions，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"> 文字</font>'''二阶相变Second-order phase transitions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。比如包括铁等材料中的铁磁相变，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连续增加。而磁化率，是自由能相对于磁场的二阶导数，它的变化则是不连续的。以此类推，按照埃伦费斯特的分类方法，原则上可以存在第三，第四和更高阶的相变。

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.

埃伦费斯特分类法Ehrenfest classification隐含了连续的相变，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"> 文字</font>'''埃伦费斯特分类法Ehrenfest classification隐含了连续的相变，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。

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.

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.

一阶相变是那些涉及潜伏热的相变。在这种相变过程中，系统会吸收或释放每体积固定（通常是大量）的能量。在此过程中，系统的温度将随着热量的增加而保持恒定：系统处于“混合相状态”，其中系统的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，而是形成液态水和蒸气气泡的湍流混合物）。物理学家Imry和Wortis研究表明，淬火无序Quenched disorder可以视为一阶转变。即在有限的温度范围内完成了相的转变，但是诸如过冷和过热的现象仍然存在，并且在热循环中观察到了滞后。

一阶相变是那些涉及潜伏热的相变。在这种相变过程中，系统会吸收或释放每体积固定（通常是大量）的能量。在此过程中，系统的温度将随着热量的增加而保持恒定：系统处于“混合相状态”，其中系统的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，而是形成液态水和蒸气气泡的湍流混合物）。物理学家Imry和Wortis研究表明，'''<font color="#ff8000"> 文字</font>'''淬火无序Quenched disorder可以视为一阶转变。即在有限的温度范围内完成了相的转变，但是诸如过冷和过热的现象仍然存在，并且在热循环中观察到了滞后。

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.

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.

另外还存在其他相变类型例如无序相变。无序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Kosterlitz-Thouless相变。除此之外二维电子气中的量子相变也都属于此类。

另外还存在其他相变类型例如无序相变。无序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"> 文字</font>'''Kosterlitz-Thouless相变。除此之外二维电子气中的量子相变也都属于此类。

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).

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).

相变通常涉及到对称破坏。例如，将流体冷却至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，但是晶体中的每个点都不具有相同的属性（除非这些点是从晶格点阵的晶格点中选择的）。通常，由于自发对称性破缺Spontaneous symmetry breaking，除了某些偶然的对称性（例如，重虚粒子Virtual particles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，但是晶体中的每个点都不具有相同的属性（除非这些点是从晶格点阵的晶格点中选择的）。通常，由于'''<font color="#ff8000"> 文字</font>'''自发对称性破缺Spontaneous symmetry breaking，除了某些偶然的对称性（例如，重虚粒子Virtual particles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。

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 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.

序参数Order parameter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）与另一个非零阶段之间。在临界点，序参数的敏感性通常会发散。

'''<font color="#ff8000"> 文字</font>'''序参数Order parameter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）与另一个非零阶段之间。在临界点，序参数的敏感性通常会发散。

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.

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 vortex- or 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.

就无序参数而言，也存在相变的双重描述。 这些表明存在线状激励line-like excitations，例如涡旋线vortex lines或缺陷线defect lines。

就无序参数而言，也存在相变的双重描述。 这些表明存在'''<font color="#ff8000"> 文字</font>'''线状激励line-like excitations，例如'''<font color="#ff8000"> 文字</font>'''涡旋线vortex lines或'''<font color="#ff8000"> 文字</font>'''缺陷线defect lines。

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).

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).

对称破坏性的相变在宇宙学中起着重要作用。随着宇宙的膨胀和冷却，真空经历了一系列对称破坏的相变。例如，电弱过渡将电弱场的''SU（2）×U（1）''对称性破坏为当今电磁场的''U（1）''对称性。这种转变对于理解当今宇宙中物质与反物质之间的不对称性很重要（请参阅弱电重子生成Electroweak baryogenesis）。

对称破坏性的相变在宇宙学中起着重要作用。随着宇宙的膨胀和冷却，真空经历了一系列对称破坏的相变。例如，电弱过渡将电弱场的''SU（2）×U（1）''对称性破坏为当今电磁场的''U（1）''对称性。这种转变对于理解当今宇宙中物质与反物质之间的不对称性很重要（请参阅'''<font color="#ff8000"> 文字</font>'''弱电重子生成Electroweak baryogenesis）。

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.

由于不存在潜伏热Latent heat，连续相变比一阶相变更容易研究，目前发现它们具有许多有趣的性质。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"> 文字</font>'''潜伏热Latent heat，连续相变比一阶相变更容易研究，目前发现它们具有许多有趣的性质。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。

It is widely believed  that the critical exponents are the same above and below the critical temperature. It has now been shown that this is not necessarily true: When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as <math>\gamma </math>, the exponent of the susceptibility) are not identical.

It is widely believed  that the critical exponents are the same above and below the critical temperature. It has now been shown that this is not necessarily true: When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as <math>\gamma </math>, the exponent of the susceptibility) are not identical.

之前普遍认为，临界指数在临界温度上下浮动的时候都是相同的。但是现已证明其不一定正确：因不相关的各向异性（在重整化群理论意义上）将连续对称属性清晰地分解为离散对称属性时，则某些指数（例如γ，磁化率指数Exponent of the susceptibility）不相同。

之前普遍认为，临界指数在临界温度上下浮动的时候都是相同的。但是现已证明其不一定正确：因不相关的各向异性（在重整化群理论意义上）将连续对称属性清晰地分解为离散对称属性时，则某些指数（例如γ，'''<font color="#ff8000"> 文字</font>'''磁化率指数Exponent of the susceptibility）不相同。

Several other critical exponents, , and , are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations, such as

Several other critical exponents, , and , are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations, such as

<math>\beta=\gamma/(\delta-1) , \qquad \nu=\gamma/(2-\eta)</math>.

<math>\beta=\gamma/(\delta-1) , \qquad \nu=\gamma/(2-\eta)</math>.

It can be shown that there are only two independent exponents, e.g. {{mvar|ν}} and {{mvar|η}}.

It can be shown that there are only two independent exponents, e.g. {{mvar|ν}} and {{mvar|η}}.

It can be shown that there are only two independent exponents, e.g.  and .

It can be shown that there are only two independent exponents, e.g.  and .

上式可以证明只有两个独立的指数，例如 ν和η。

上式可以证明只有两个独立的指数，例如 ''ν''和''η''。

Another phenomenon which shows phase transitions and critical exponents is percolation. The simplest example is perhaps percolation in a two dimensional square lattice. Sites are randomly occupied with probability p. For small values of p the occupied sites form only small clusters. At a certain threshold p_c a giant cluster is formed and we have a second-order phase transition. The behavior of P_∞ near p_c is, P_∞~(p-p_c)^β, where β is a critical exponent.

Another phenomenon which shows phase transitions and critical exponents is percolation. The simplest example is perhaps percolation in a two dimensional square lattice. Sites are randomly occupied with probability p. For small values of p the occupied sites form only small clusters. At a certain threshold p_c a giant cluster is formed and we have a second-order phase transition. The behavior of P_∞ near p_c is, P_∞~(p-p_c)^β, where β is a critical exponent.

显示相变和临界指数的另一种现象是渗流。最简单的例子是发生在二维方格中的渗流。其中每一个格子以概率p标记。对于较小的p值，标记的格子仅形成较小的团簇。但是当p达到某个阈值pc时会形成一个巨大的团簇，此时发生二阶相变。pc附近的P∞行为是P∞〜（p − pc）β，其中β是一个临界指数。

显示相变和临界指数的另一种现象是渗流。最简单的例子是发生在二维方格中的渗流。其中每一个格子以概率''p''标记。对于较小的''p''值，标记的格子仅形成较小的团簇。但是当p达到某个阈值''Pc''时会形成一个巨大的团簇，此时发生二阶相变。''Pc''附近的P∞行为是''P∞〜（p − pc）β''，其中β是一个临界指数。

Phase transitions play many important roles in biological systems. Examples include the lipid bilayer formation, the coil-globule transition in the process of protein folding and DNA melting, liquid crystal-like transitions in the process of DNA condensation, and cooperative ligand binding to DNA and proteins with the character of phase transition.

Phase transitions play many important roles in biological systems. Examples include the lipid bilayer formation, the coil-globule transition in the process of protein folding and DNA melting, liquid crystal-like transitions in the process of DNA condensation, and cooperative ligand binding to DNA and proteins with the character of phase transition.

相变在生物系统中也起到许多重要的作用。比如包括脂质双层Lipid bilayer的形成，蛋白质折叠Protein folding和DNA解链DNA melting过程中的坍塌转变Coil–globule transition，DNA缩合DNA condensation过程中的液晶转变，以及具有相变特征的配体与DNA和蛋白质的结合配体。

相变在生物系统中也起到许多重要的作用。比如包括'''<font color="#ff8000"> 文字</font>'''脂质双层Lipid bilayer的形成，'''<font color="#ff8000"> 文字</font>'''蛋白质折叠Protein folding和'''<font color="#ff8000"> 文字</font>'''DNA解链DNA melting过程中的'''<font color="#ff8000"> 文字</font>'''坍塌转变Coil–globule transition，'''<font color="#ff8000"> 文字</font>'''DNA缩合DNA condensation过程中的液晶转变，以及具有相变特征的配体与DNA和蛋白质的结合配体。

In biological membranes, gel to liquid crystalline phase transitions play a critical role in physiological functioning of biomembranes. In gel phase, due to low fluidity of membrane lipid fatty-acyl chains, membrane proteins have restricted movement and thus are restrained in exercise of their physiological role. Plants depend critically on photosynthesis by chloroplast thylakoid membranes which are exposed cold environmental temperatures. Thylakoid membranes retain innate fluidity even at relatively low temperatures because of high degree of fatty-acyl disorder allowed by their high content of linolenic acid, 18-carbon chain with 3-double bonds. Gel-to-liquid crystalline phase transition temperature of biological membranes can be determined by many techniques including calorimetry, fluorescence, spin label electron paramagnetic resonance and NMR by recording measurements of the concerned parameter by at series of sample temperatures. A simple method for its determination from 13-C NMR line intensities has also been proposed.

In biological membranes, gel to liquid crystalline phase transitions play a critical role in physiological functioning of biomembranes. In gel phase, due to low fluidity of membrane lipid fatty-acyl chains, membrane proteins have restricted movement and thus are restrained in exercise of their physiological role. Plants depend critically on photosynthesis by chloroplast thylakoid membranes which are exposed cold environmental temperatures. Thylakoid membranes retain innate fluidity even at relatively low temperatures because of high degree of fatty-acyl disorder allowed by their high content of linolenic acid, 18-carbon chain with 3-double bonds. Gel-to-liquid crystalline phase transition temperature of biological membranes can be determined by many techniques including calorimetry, fluorescence, spin label electron paramagnetic resonance and NMR by recording measurements of the concerned parameter by at series of sample temperatures. A simple method for its determination from 13-C NMR line intensities has also been proposed.

在生物膜Biological membranes中，凝胶到液晶的相变在生物膜的生理机能中起关键作用。在凝胶相中，由于膜脂质脂肪酰基链的流动性低，膜蛋白的运动受到限制，因此在行使其生理作用方面受到限制。植物非常依赖于暴露于寒冷环境温度下叶绿体类囊体膜的光合作用。类囊体膜即使在相对较低的温度下也能保持固有的流动性，这是由于其高含量的亚麻酸，带有3个双键的18碳链允许高度的脂肪酰基紊乱。基于众多技术，包括量热法，荧光法，自旋标记电子顺磁共振和NMR，通过记录一系列样品温度下有关参数的测量值，来确定生物膜的凝胶到液晶的相变温度。同时还提出了一种由13-C NMR谱线强度测定的简单方法。

在'''<font color="#ff8000"> 文字</font>'''生物膜Biological membranes中，凝胶到液晶的相变在生物膜的生理机能中起关键作用。在凝胶相中，由于膜脂质脂肪酰基链的流动性低，膜蛋白的运动受到限制，因此在行使其生理作用方面受到限制。植物非常依赖于暴露于寒冷环境温度下叶绿体类囊体膜的光合作用。类囊体膜即使在相对较低的温度下也能保持固有的流动性，这是由于其高含量的亚麻酸，带有3个双键的18碳链允许高度的脂肪酰基紊乱。基于众多技术，包括量热法，荧光法，自旋标记电子顺磁共振和NMR，通过记录一系列样品温度下有关参数的测量值，来确定生物膜的凝胶到液晶的相变温度。同时还提出了一种由13-C NMR谱线强度测定的简单方法。

* [[Perturbed angular correlation]] (simultaneous measurement of magnetic and non-magnetic transitions. No temperature limits. Over 2000&nbsp;°C already performed, theoretical possible up to the highest crystal material, such as [[tantalum hafnium carbide]] 4215&nbsp;°C.)

* [[Perturbed angular correlation]] (simultaneous measurement of magnetic and non-magnetic transitions. No temperature limits. Over 2000&nbsp;°C already performed, theoretical possible up to the highest crystal material, such as [[tantalum hafnium carbide]] 4215&nbsp;°C.)

•扰动角关联（同时测量磁性和非磁性跃迁。没有温度限制。已经执行了超过2000°C的操作，理论上可能达到最高晶体材料，例如钽碳化carbide 4215°C。）

•'''<font color="#ff8000"> 文字</font>'''扰动角关联（同时测量磁性和非磁性跃迁。没有温度限制。已经执行了超过2000°C的操作，理论上可能达到最高晶体材料，例如钽碳化carbide 4215°C。）

* [[Allotropy 同素异形体]]

* [['''<font color="#ff8000"> 文字</font>'''Allotropy 同素异形体]]

* [[Autocatalytic reactions and order creation 自动催化反应和序生成]]

* [['''<font color="#ff8000"> 文字</font>'''Autocatalytic reactions and order creation 自动催化反应和序生成]]

* [[Crystal growth 晶体生长]]

* [['''<font color="#ff8000"> 文字</font>'''Crystal growth 晶体生长]]

** [[Abnormal grain growth 谷物异常生长]]

** [['''<font color="#ff8000"> 文字</font>'''Abnormal grain growth 谷物异常生长]]

* [[Differential scanning calorimetry 差示扫描量热法]]

* [['''<font color="#ff8000"> 文字</font>'''Differential scanning calorimetry 差示扫描量热法]]

* [[Diffusionless transformations 无扩散相变]]

* [['''<font color="#ff8000"> 文字</font>'''Diffusionless transformations 无扩散相变]]

* [[Ehrenfest equations 埃伦费斯特方程]]

* [['''<font color="#ff8000"> 文字</font>'''Ehrenfest equations 埃伦费斯特方程]]

* [[Jamming (physics) 阻塞（物理）]]

* [['''<font color="#ff8000"> 文字</font>'''Jamming (physics) 阻塞（物理）]]

* [[Kelvin probe force microscope 开尔文探针力显微镜]]

* [['''<font color="#ff8000"> 文字</font>'''Kelvin probe force microscope 开尔文探针力显微镜]]

* [[Landau theory of second order phase transition]] 朗道二阶相变理论

* [['''<font color="#ff8000"> 文字</font>'''Landau theory of second order phase transition]] 朗道二阶相变理论

* [[Laser-heated pedestal growth 激光加热基座法]]

* [['''<font color="#ff8000"> 文字</font>'''Laser-heated pedestal growth 激光加热基座法]]

* [[List of states of matter 物质状态列表]]

* [['''<font color="#ff8000"> 文字</font>'''List of states of matter 物质状态列表]]

* [[Micro-pulling-down 微下拉法]]

* [['''<font color="#ff8000"> 文字</font>'''Micro-pulling-down 微下拉法]]

* [[Percolation theory 渗流理论]]

* [['''<font color="#ff8000"> 文字</font>'''Percolation theory 渗流理论]]

** [[Continuum percolation theory 连续介质渗流理论]]

** [['''<font color="#ff8000"> 文字</font>'''Continuum percolation theory 连续介质渗流理论]]

* [[Superfluid film 超流体膜]]

* [['''<font color="#ff8000"> 文字</font>'''Superfluid film 超流体膜]]

* [[Superradiant phase transition 超辐射相变]]

* [['''<font color="#ff8000"> 文字</font>'''Superradiant phase transition 超辐射相变]]

* [[Topological quantum field theory 拓扑量子场论]]

* [['''<font color="#ff8000"> 文字</font>'''Topological quantum field theory 拓扑量子场论]]

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