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第444行：
第444行： − + − The anomalous dimensions in certain two-dimensional CFTs can be related to the typical fractal dimensions of random walks, where the random walks are defined via Schramm–Loewner evolution (SLE). As we have seen above, CFTs describe the physics of phase transitions, and so one can relate the critical exponents of certain phase transitions to these fractal dimensions. Examples include the 2d critical Ising model and the more general 2d critical Potts model. Relating other 2d CFTs to SLE is an active area of research.+ − − 某些二维 CFTs 的异常维数可能与随机游动的典型分形维数有关，其中随机游动是通过施拉姆-洛沃纳演化(SLE)定义的。正如我们上面所看到的，CFTs 描述了相变的物理过程，因此我们可以把某些相变的临界指数与这些分形维数联系起来。例子包括二维临界 Ising 模型和更一般的二维临界 Potts 模型。关联其他2 d cft 与系统性红斑狼疮是一个积极的研究领域。 第456行：
第454行： − A phenomenon known as universality is seen in a large variety of physical systems. It expresses the idea that different microscopic physics can give rise to the same scaling behaviour at a phase transition. A canonical example of universality involves the following two systems:+ − * The Ising model phase transition, described above. − * The liquid-vapour transition in classical fluids. − − 在各种各样的物理系统中都可以看到一种被称为普遍性的现象。它表达了不同的微观物理学可以在相变过程中产生相同的标度行为的观点。普适性的一个典型例子涉及以下两个系统: 第466行：
第460行： − Even though the microscopic physics of these two systems is completely different, their critical exponents turn out to be the same. Moreover, one can calculate these exponents using the same statistical field theory. The key observation is that at a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for a scale-invariant statistical field theory to describe the phenomena. In a sense, universality is the observation that there are relatively few such scale-invariant theories.+ − − 尽管这两个系统的微观物理学完全不同，但它们的临界指数却是相同的。此外，我们可以使用相同的统计场理论计算这些指数。关键的观察结果是，在相变或临界点，在所有长度尺度上都会出现波动，因此我们应该寻找一个尺度不变的统计场理论来描述这种现象。从某种意义上说，普适性就是观察到这样的尺度不变理论相对较少。
→Schramm–Loewner evolution
<math>\eta_{_{D=2}}=\frac{1}{4}</math>
<math>\eta_{_{D=2}}=\frac{1}{4}</math>
===Schramm–Loewner evolution===
===Schramm–Loewner evolution 施拉姆—洛纳演化===
The anomalous dimensions in certain two-dimensional CFTs can be related to the typical [[fractal dimension]]s of random walks, where the random walks are defined via [[Schramm–Loewner evolution]] (SLE). As we have seen above, CFTs describe the physics of phase transitions, and so one can relate the critical exponents of certain phase transitions to these fractal dimensions. Examples include the 2''d'' critical Ising model and the more general 2''d'' critical [[Potts model]]. Relating other 2''d'' CFTs to SLE is an active area of research.
The anomalous dimensions in certain two-dimensional CFTs can be related to the typical [[fractal dimension]]s of random walks, where the random walks are defined via [[Schramm–Loewner evolution]] (SLE). As we have seen above, CFTs describe the physics of phase transitions, and so one can relate the critical exponents of certain phase transitions to these fractal dimensions. Examples include the 2''d'' critical Ising model and the more general 2''d'' critical [[Potts model]]. Relating other 2''d'' CFTs to SLE is an active area of research.
某些二维共形场论的异常维数可能与随机游动的典型分形维数有关，其中随机游动是通过施拉姆-洛纳演化(SLE)定义的。正如我们上面所看到的，共形场论描述了相变的物理过程，因此我们可以把某些相变的临界指数与这些分形维数联系起来。例如，二维临界伊辛模型和更一般的二维临界波茨模型。将其他二维共形场论与施拉姆-洛纳演化联系起来是一个活跃的研究领域。
==Universality 普适性==
==Universality 普适性==
* The [[liquid]]-[[vapour]] transition in classical fluids.
* The [[liquid]]-[[vapour]] transition in classical fluids.
普适性的现象存在于许多不同的物理系统中。它表达了不同的微观物理过程可以在相变中产生相同的标度行为的观点。普适性的典型例子涉及以下两个系统:
* 伊辛模型相变，如上所述。
* 伊辛模型相变，如上所述。
* 经典流体中的液-气转变。
* 经典流体中的液-气转变。
Even though the microscopic physics of these two systems is completely different, their critical exponents turn out to be the same. Moreover, one can calculate these exponents using the same statistical field theory. The key observation is that at a phase transition or [[critical point (thermodynamics)|critical point]], fluctuations occur at all length scales, and thus one should look for a scale-invariant statistical field theory to describe the phenomena. In a sense, universality is the observation that there are relatively few such scale-invariant theories.
Even though the microscopic physics of these two systems is completely different, their critical exponents turn out to be the same. Moreover, one can calculate these exponents using the same statistical field theory. The key observation is that at a phase transition or [[critical point (thermodynamics)|critical point]], fluctuations occur at all length scales, and thus one should look for a scale-invariant statistical field theory to describe the phenomena. In a sense, universality is the observation that there are relatively few such scale-invariant theories.
尽管这两个系统的微观物理过程完全不同，但它们的临界指数却是相同的。此外，我们可以使用相同的统计场论计算这些指数。在相变或临界点，值得我们注意的是，在所有长度标度上都会出现波动，因此我们应该寻找一个标度不变的统计场论来描述这种现象。从某种意义上说，普适性就是指观察到这样的标度不变理论相对稀少。
The set of different microscopic theories described by the same scale-invariant theory is known as a [[universality class]]. Other examples of systems which belong to a universality class are:
The set of different microscopic theories described by the same scale-invariant theory is known as a [[universality class]]. Other examples of systems which belong to a universality class are: