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| − | Several other critical exponents, {{math| ''β, γ, δ, ν''}}, and {{mvar|η}}, are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations, such as
| + | 另外还存在其他几个临界指数{{math| ''β, γ, δ, ν''}}和{{mvar|η}}，主要用于检查相变附近可测物理量的幂律行为。它们通过比例关系相互联系，例如： |
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| − | 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
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| − | 另外还存在其他几个临界指数''β，γ，δ，ν''和''η''，主要用于检查相变附近可测物理量的幂律行为。它们通过比例关系相互联系，例如：
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| | <math>\beta=\gamma/(\delta-1) , \qquad \nu=\gamma/(2-\eta)</math>. | | <math>\beta=\gamma/(\delta-1) , \qquad \nu=\gamma/(2-\eta)</math>. |
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| − | It can be shown that there are only two independent exponents, e.g. {{mvar|ν}} and {{mvar|η}}.
| + | 上式可以证明只有两个独立的指数，例如 {{mvar|ν}}和 {{mvar|η}}。 |
| − | It can be shown that there are only two independent exponents, e.g. and .
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| − | 上式可以证明只有两个独立的指数，例如 ''ν''和''η''。
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| − | 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.
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| − | 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.
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| | 值得注意的是，在不同系统中发生的相变通常具有相同的临界指数。我们称这种现象为'''<font color="#ff8000">普适性universality</font>'''。例如，液气临界点的临界指数与流体的化学组成无关。 | | 值得注意的是，在不同系统中发生的相变通常具有相同的临界指数。我们称这种现象为'''<font color="#ff8000">普适性universality</font>'''。例如，液气临界点的临界指数与流体的化学组成无关。 |
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| − | | + | 以上现象很特别，但并非无法理解，它们与单轴磁体中铁磁相变的临界指数完全匹配。人们认为这类系统具有同一普适性。这里的普适性是相变的[[重整化群理论]]的一种预测，指出系统在即将相变时的热力学性质仅取决于少数几个特征，例如'''<font color="#ff8000">维数dimensionality</font>'''和'''<font color="#ff8000">对称性symmetry</font>'''，对系统的基本微观特性并不敏感。同样，相关长度的差异性也是非常重要的因素。 |
| − | 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.
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| − | 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.
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| − | 以上现象很特别，但并非无法理解，它们与单轴磁体中铁磁相变的临界指数完全匹配。人们认为这类系统具有同一普适性。这里的普适性是相变的重整化群理论的一种预测，指出系统在即将相变时的热力学性质仅取决于少数几个特征，例如'''<font color="#ff8000">维数dimensionality</font>'''和'''<font color="#ff8000">对称性symmetry</font>'''，对系统的基本微观特性并不敏感。同样，相关长度的差异性也是非常重要的因素。
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| | === Critical slowing down and other phenomena 临界慢化和其他现象 === | | === Critical slowing down and other phenomena 临界慢化和其他现象 === |