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→Quenched disorder
In statistical physics, a system is said to present quenched disorder when some parameters defining its behavior are random variables which do not evolve with time, i.e. they are quenched or frozen. Spin glasses are a typical example. It is opposite to annealed disorder, where the random variables are allowed to evolve themselves.
In statistical physics, a system is said to present quenched disorder when some parameters defining its behavior are random variables which do not evolve with time, i.e. they are quenched or frozen. Spin glasses are a typical example. It is opposite to annealed disorder, where the random variables are allowed to evolve themselves.
在'''<font color="#ff8000">统计物理 Statistical Physics</font>'''中，当定义系统行为的某些参数是不随时间演化的'''<font color="#ff8000">随机变量 Random Variable</font>'''时，系统称为淬致无序。它们被'''<font color="#ff8000">淬火 Quenched</font>'''或者''冷冻''。'''<font color="#ff8000">自旋玻璃 Spin Glass</font>'''就是一个典型的例子。与'''<font color="#ff8000">退火无序 Annealed Disorder</font>'''相反，随机变量允许自身进化。
在'''<font color="#ff8000">统计物理学 Statistical Physics</font>'''中，当定义系统行为的某些参数是不随时间演化的'''<font color="#ff8000">随机变量 Random Variable</font>'''时，系统称为淬致无序。它们被'''<font color="#ff8000">淬火 Quenched</font>'''或者''冷冻''。'''<font color="#ff8000">自旋玻璃 Spin Glass</font>'''就是一个典型的例子。与'''<font color="#ff8000">退火无序 Annealed Disorder</font>'''相反，随机变量允许自身进化。
In mathematical terms, quenched disorder is harder to analyze than its annealed counterpart, since the thermal and the noise averaging play very different roles. In fact, the problem is so hard that few techniques to approach each are known, most of them relying on approximations. The most used are
In mathematical terms, quenched disorder is harder to analyze than its annealed counterpart, since the thermal and the noise averaging play very different roles. In fact, the problem is so hard that few techniques to approach each are known, most of them relying on approximations. The most used are
在数学中，淬致无序比退火无序更难分析，因为热平均和噪声通常起着非常不同的作用。事实上，这个问题是如此的困难，以至于很少有已知的技术可以处理任何一个问题，大多数解决方案都依赖于近似值。最常用的是
the Cavity method; although these give results in accord with experiments in a large range of problems, they are not generally proven to be a rigorous mathematical procedure.
the Cavity method; although these give results in accord with experiments in a large range of problems, they are not generally proven to be a rigorous mathematical procedure.
'''<font color="#ff8000">谐振腔法 Cavity Method</font>'''：虽然这些方法给出的结果与许多问题的实验结果相一致，但它们通常不被证明是一个严格的数学过程。
'''<font color="#ff8000">谐振腔法 Cavity Method</font>'''：虽然这些方法给出的结果与许多问题的实验结果相一致，但它们通常不是一个可证明的严格数学过程。
More recently it has been shown by rigorous methods, however, that at least in the archetypal spin-glass model (the so-called Sherrington–Kirkpatrick model) the replica based solution is indeed exact.
More recently it has been shown by rigorous methods, however, that at least in the archetypal spin-glass model (the so-called Sherrington–Kirkpatrick model) the replica based solution is indeed exact.
然而，最近人们已经通过严密的方法证明，至少在典型的自旋玻璃模型(所谓的 '''<font color="#ff8000">Sherrington–Kirkpatrick 模型 Sherrington–Kirkpatrick Model</font>''')中，基于复制的解确实是精确的。
The second most used technique in this field is generating functional analysis. This method is based on path integrals, and is in principle fully exact, although generally more difficult to apply than the replica procedure.
The second most used technique in this field is generating functional analysis. This method is based on path integrals, and is in principle fully exact, although generally more difficult to apply than the replica procedure.
该领域第二常用的技术是'''<font color="#ff8000">生成函数分析 Generating Functional Analysis</font>'''。这种方法是基于'''<font color="#ff8000">路线积分 Path Integrals</font>'''的，原则上是完全精确的，虽然通常比复制过程更难应用。
该领域第二常用的技术是'''<font color="#ff8000">生成函数分析 Generating Functional Analysis</font>'''。这种方法是基于'''<font color="#ff8000">路线积分 Path Integrals</font>'''的，虽然这通常比复制过程更难应用，但原则上是完全精确的，
从无序(左)状态过渡到有序(右)状态
从无序(左)状态过渡到有序(右)状态
==Annealed disorder==
==Annealed disorder==