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第403行： − 值得注意的是，在不同系统中发生的相变通常具有相同的关键指数集。这种现象称为通用性。例如，已发现液气临界点的临界指数与流体的化学组成无关。+ 第416行：
第411行： − 上方这个现象很特别但是可以理解，它们与单轴磁体中铁磁相变的临界指数完全匹配。这类系统因此被认为属于同一通用性类别。这里的通用性是相变的重整化群理论的一种预测，指出系统在相变附近的热力学性质仅取决于少数特征，例如维数和对称性，并且对系统的基本微观特性不敏感。同样，相关长度的差异性是非常重要的。+ 第426行：
第421行： − 在相变过程中，还存在其他临界现象。例如除了静态函数外，还存在关键的临界动态。因此在相变发生时，人们可能会观察到严重的减速或加速现象。连续相变的静态通用类可以分成更小的动态通用类。除了临界指数外，磁场的某些静态或动态函数以及与临界值的温差也存在通用关系。+ 第579行：
第574行： − • Anderson, P.W., 《凝聚态物理的基本概念》, Perseus Publishing (1997).+ − • Faghri, A., and Zhang, Y., 《多相传热与流动基础》, Springer Nature Switzerland AG, 2020.+ − • Fisher, M.E. (1974). “临界行为理论中的再规范化”. Rev. Mod. Phys. 46 (4): 597–616. Bibcode:1974RvMP...46..597F. doi:10.1103/revmodphys.46.597.+ − • Goldenfeld, N., 《关于相变和重整化群的讲座》, Perseus Publishing (1992).+ − • Ivancevic, Vladimir G; Ivancevic, Tijana T (2008), 《混沌，相变，拓扑变化和路径积分》, Berlin: Springer, ISBN 978-3-540-79356-4, retrieved 14 March 2013+ − • M.R.Khoshbin-e-Khoshnazar, 《冰的相变作为有限系统相变的一个样本》, (Physics Education(India)Volume 32. No. 2, Apr - Jun 2016)[1]+ − • Kleinert, H., 《凝聚物质的规范场》, Vol. I, “超流体和涡旋线；无序场，相变”, pp. 1–742, World Scientific (Singapore, 1989); Paperback ISBN 9971-5-0210-0 (readable online physik.fu-berlin.de)+ − • Kleinert, H. and Verena Schulte-Frohlinde, 《φ4-理论的临界性质》, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4659-5 (readable online here).+ − • Kogut, J.; Wilson, K (1974). “重整化群和epsilon扩展”. Phys. Rep. 12 (2): 75–199. Bibcode:1974PhR....12...75W. doi:10.1016/0370-1573(74)90023-4.+ − • Krieger, Martin H., 《物质的构成：对物理现象进行最日常的数学建模》, University of Chicago Press, 1996. 其中包含对Onsager的二维伊辛模型解决方案的详细教学讨论。+ − • Landau, L.D. and Lifshitz, E.M., 《统计物理学》 Part 1, vol. 5 of Course of Theoretical Physics, Pergamon Press, 3rd Ed. (1994).+ − • Mussardo G., “统计场论。统计物理学的精确求解模型导论”，Oxford University Press, 2010.+ − • Schroeder, Manfred R., 《分形，混沌，幂定律：距离无限天堂的分钟路程》, New York: W. H. Freeman, 1991. 写得很好的“半大众”风格的书，而不是教科书，旨在介绍数学和物理科学方面的知识。解释相变的标定是什么。+ − • H. E. Stanley, 《相变和临界现象导论》(Oxford University Press, Oxford and New York 1971).+ − • Yeomans J. M., 《相变的统计力学》, Oxford University Press, 1992.+ 第603行：
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无编辑摘要
{{Condensed matter physics|expanded=States of matter}}
{{Condensed matter physics|expanded=States of matter}}
* 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.
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，连接概率代替渗滤网络Percolating networks的温度。
在相变点（例如，沸点）下，一种物质的两个相（液体和蒸气）具有相同的自由能，因此它们可以同时存在。而当温度低于沸点时，液体在两者中状态更稳定，因此相比较气态更趋近于液态存在。
在相变点（例如，沸点）下，一种物质的两个相（液体和蒸气）具有相同的自由能，因此它们可以同时存在。而当温度低于沸点时，液体在两者中状态更稳定，因此相比较气态更趋近于液态存在。
有时可以通过传热方式（注意不是绝热方式）改变系统状态，使系统状态可以通过相变点而不会经历相变。因此该系统会处于亚稳态，是指比较于相变发生过后的状态没有那么稳定，但也不是说不稳定。
有时可以通过传热方式（注意不是绝热方式）改变系统状态，使系统状态可以通过相变点而不会经历相变。因此该系统会处于亚稳态，是指比较于相变发生过后的状态没有那么稳定，但也不是说不稳定。
== Classifications 分类==
== Classifications 分类==
=== Critical exponents and universality classes 临界指数和通用类型 ===
=== Critical exponents and universality classes 临界指数和普适性 ===
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.
<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 is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as universality. For example, the critical exponents at the liquid–gas critical point have been found to be independent of the chemical composition of the fluid.
It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as universality. For example, the critical exponents at the liquid–gas critical point have been found to be independent of the chemical composition of the fluid.
值得注意的是，在不同系统中发生的相变通常具有相同的关键指数集。这种现象称为普适性。例如，已发现液气临界点的临界指数与流体的化学组成无关。
More impressively, but understandably from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the renormalization group theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. Again, the divergence of the correlation length is the essential point.
More impressively, but understandably from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the renormalization group theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. Again, the divergence of the correlation length is the essential point.
上方这个现象很特别但是可以理解，它们与单轴磁体中铁磁相变的临界指数完全匹配。这类系统因此被认为属于同一普适性。这里的普适性是相变的重整化群理论的一种预测，指出系统在相变附近的热力学性质仅取决于少数特征，例如维数和对称性，并且对系统的基本微观特性不敏感。同样，相关长度的差异性是非常重要的。
There are also other critical phenomena; e.g., besides static functions there is also critical dynamics. As a consequence, at a phase transition one may observe critical slowing down or speeding up. The large static universality classes of a continuous phase transition split into smaller dynamic universality classes. In addition to the critical exponents, there are also universal relations for certain static or dynamic functions of the magnetic fields and temperature differences from the critical value.
There are also other critical phenomena; e.g., besides static functions there is also critical dynamics. As a consequence, at a phase transition one may observe critical slowing down or speeding up. The large static universality classes of a continuous phase transition split into smaller dynamic universality classes. In addition to the critical exponents, there are also universal relations for certain static or dynamic functions of the magnetic fields and temperature differences from the critical value.
在相变过程中，还存在其他临界现象。例如除了静态函数外，还存在关键的临界动态。因此在相变发生时，人们可能会观察到严重的减速或加速现象。连续相变的静态普适性可以分成更小的动态普适性。除了临界指数外，磁场的某些静态或动态函数以及与临界值的温差也存在普适性关系。
* Anderson, P.W., 《凝聚态物理的基本概念》, Perseus Publishing (1997).
* Faghri, A., and Zhang, Y., 《多相传热与流动基础》, Springer Nature Switzerland AG, 2020.
* Fisher, M.E. (1974). “临界行为理论中的再规范化”. Rev. Mod. Phys. 46 (4): 597–616. Bibcode:1974RvMP...46..597F. doi:10.1103/revmodphys.46.597.
* Goldenfeld, N., 《关于相变和重整化群的讲座》, Perseus Publishing (1992).
* Ivancevic, Vladimir G; Ivancevic, Tijana T (2008), 《混沌，相变，拓扑变化和路径积分》, Berlin: Springer, ISBN 978-3-540-79356-4, retrieved 14 March 2013
* M.R.Khoshbin-e-Khoshnazar, 《冰的相变作为有限系统相变的一个样本》, (Physics Education(India)Volume 32. No. 2, Apr - Jun 2016)[1]
* Kleinert, H., 《凝聚物质的规范场》, Vol. I, “超流体和涡旋线；无序场，相变”, pp. 1–742, World Scientific (Singapore, 1989); Paperback ISBN 9971-5-0210-0 (readable online physik.fu-berlin.de)
* Kleinert, H. and Verena Schulte-Frohlinde, 《φ4-理论的临界性质》, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4659-5 (readable online here).
* Kogut, J.; Wilson, K (1974). “重整化群和epsilon扩展”. Phys. Rep. 12 (2): 75–199. Bibcode:1974PhR....12...75W. doi:10.1016/0370-1573(74)90023-4.
* Krieger, Martin H., 《物质的构成：对物理现象进行最日常的数学建模》, University of Chicago Press, 1996. 其中包含对Onsager的二维伊辛模型解决方案的详细教学讨论。
* Landau, L.D. and Lifshitz, E.M., 《统计物理学》 Part 1, vol. 5 of Course of Theoretical Physics, Pergamon Press, 3rd Ed. (1994).
* Mussardo G., “统计场论。统计物理学的精确求解模型导论”，Oxford University Press, 2010.
* Schroeder, Manfred R., 《分形，混沌，幂定律：距离无限天堂的分钟路程》, New York: W. H. Freeman, 1991. 写得很好的“半大众”风格的书，而不是教科书，旨在介绍数学和物理科学方面的知识。解释相变的标定是什么。
* H. E. Stanley, 《相变和临界现象导论》(Oxford University Press, Oxford and New York 1971).
* Yeomans J. M., 《相变的统计力学》, Oxford University Press, 1992.
*[http://www.ibiblio.org/e-notes/Perc/contents.htm Interactive Phase Transitions on lattices] with Java applets 使用Java小程序在晶格上进行交互式相变
*[http://www.ibiblio.org/e-notes/Perc/contents.htm Interactive Phase Transitions on lattices] with Java applets 使用Java小程序在晶格上进行交互式相变
*[http://www.sklogwiki.org/SklogWiki/index.php/Universality_classes Universality classes 通用类] from Sklogwiki
*[http://www.sklogwiki.org/SklogWiki/index.php/Universality_classes Universality classes 普适性分类] from Sklogwiki
{{States of matter}}
{{States of matter}}