596
个编辑
更改
跳到导航
跳到搜索
第370行：
第370行： − + − An example that links together many of the ideas in this article is the phase transition of the Ising model, a simple model of ferromagnetic substances. This is a statistical mechanics model, which also has a description in terms of conformal field theory. The system consists of an array of lattice sites, which form a -dimensional periodic lattice. Associated with each lattice site is a magnetic moment, or spin, and this spin can take either the value +1 or −1. (These states are also called up and down, respectively.)+ − − 将本文中的许多观点联系在一起的一个例子是伊辛模型的相变，这是一个铁磁物质的简单模型。这是一个统计力学的模型，也有一个描述的共形场论。该系统由一系列晶格位点组成，这些位点构成了一个维的周期晶格。与每个晶格位置相关联的是磁矩或自旋，这个自旋可以取 + 1或-1。(这些状态也分别称为上升和下降。) − The key point is that the Ising model has a spin-spin interaction, making it energetically favourable for two adjacent spins to be aligned. On the other hand, thermal fluctuations typically introduce a randomness into the alignment of spins. At some critical temperature, , spontaneous magnetization is said to occur. This means that below the spin-spin interaction will begin to dominate, and there is some net alignment of spins in one of the two directions.+ − − 关键点在于伊辛模型具有自旋-自旋相互作用，使其能量上有利于两个相邻的自旋对齐。另一方面，热涨落通常在自旋排列中引入一种随机性。在某些临界温度下，据说会发生自发磁化。这意味着在自旋-自旋相互作用下将开始占主导地位，并且在两个方向之一存在一些自旋的网络排列。
→The Ising model Ising 模型
在统计力学中，当某个系统经历相变时，其波动可以用标度不变的统计场论来描述。对于在{{mvar|D}}空间维度中处于平衡状态(即时间无关)的系统，相应的统计场论形式上类似于{{mvar|D}}维共形场论。这类问题中的标度维数通常称为'''Critical Exponents 临界指数'''，原则上可以在适当的共形场论中计算这些指数。
在统计力学中，当某个系统经历相变时，其波动可以用标度不变的统计场论来描述。对于在{{mvar|D}}空间维度中处于平衡状态(即时间无关)的系统，相应的统计场论形式上类似于{{mvar|D}}维共形场论。这类问题中的标度维数通常称为'''Critical Exponents 临界指数'''，原则上可以在适当的共形场论中计算这些指数。
===The Ising model Ising 模型===
===The Ising model 伊辛模型===
An example that links together many of the ideas in this article is the phase transition of the [[Ising model]], a simple model of [[ferromagnet]]ic substances. This is a statistical mechanics model, which also has a description in terms of conformal field theory. The system consists of an array of lattice sites, which form a {{mvar|D}}-dimensional periodic lattice. Associated with each lattice site is a [[magnetic moment]], or [[spin (physics)|spin]], and this spin can take either the value +1 or −1. (These states are also called up and down, respectively.)
An example that links together many of the ideas in this article is the phase transition of the [[Ising model]], a simple model of [[ferromagnet]]ic substances. This is a statistical mechanics model, which also has a description in terms of conformal field theory. The system consists of an array of lattice sites, which form a {{mvar|D}}-dimensional periodic lattice. Associated with each lattice site is a [[magnetic moment]], or [[spin (physics)|spin]], and this spin can take either the value +1 or −1. (These states are also called up and down, respectively.)
将本文中的许多观点联系在一起的一个实例是伊辛模型的相变，这是一个关于铁磁物质的简单模型。还是一个具有共形场论描述的统计力学模型。该系统由一系列格子点位组成，这些点位构成了一个{{mvar|D}}维的周期格子。与每个格子位置相关联的是磁矩或自旋，这个自旋可以取 +1或-1。(这些状态也分别称为向上和向下。)
The key point is that the Ising model has a spin-spin interaction, making it energetically favourable for two adjacent spins to be aligned. On the other hand, thermal fluctuations typically introduce a randomness into the alignment of spins. At some critical temperature, {{math|''T<sub>c</sub>''}} , [[spontaneous magnetization]] is said to occur. This means that below {{math|''T<sub>c</sub>''}} the spin-spin interaction will begin to dominate, and there is some net alignment of spins in one of the two directions.
The key point is that the Ising model has a spin-spin interaction, making it energetically favourable for two adjacent spins to be aligned. On the other hand, thermal fluctuations typically introduce a randomness into the alignment of spins. At some critical temperature, {{math|''T<sub>c</sub>''}} , [[spontaneous magnetization]] is said to occur. This means that below {{math|''T<sub>c</sub>''}} the spin-spin interaction will begin to dominate, and there is some net alignment of spins in one of the two directions.
关键地是，伊辛模型具有自旋-自旋相互作用，这使得两个相邻的自旋在能量上更有利于排列。另一方面，热波动通常会给自旋的排列带来随机性。在某些临界温度(Tc)下，就会发生'''Spontaneous Magnetization 自发磁化'''。这意味着在临界温度以下，自旋-自旋相互作用将开始占据主导地位，并且在两个方向中的任一方向上存在部分自旋的净排列。
An example of the kind of physical quantities one would like to calculate at this critical temperature is the correlation between spins separated by a distance {{mvar|r}}. This has the generic behaviour:
An example of the kind of physical quantities one would like to calculate at this critical temperature is the correlation between spins separated by a distance {{mvar|r}}. This has the generic behaviour: