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第213行： + − It is widely believed that the critical exponents are the same above and below the critical temperature. It has now been shown that this is not necessarily true: When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as <math>\gamma </math>, the exponent of the susceptibility) are not identical. − It is widely believed that the critical exponents are the same above and below the critical temperature. It has now been shown that this is not necessarily true: When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as <math>\gamma </math>, the exponent of the susceptibility) are not identical.+ − 人们曾普遍认为，不管温度在临界温度之上还是临界温度之下，临界指数保持不变。但是现实证明这不一定正确：当连续对称属性因不相关的'''<font color="#ff8000">各向异性anisotropies</font>'''（在'''<font color="#ff8000">重整化群理论renormalization group</font>'''意义上）而分解为离散对称属性时，某些指数（例如γ，'''<font color="#ff8000"> 磁化率指数Exponent of the susceptibility</font>'''）会有所不同。 − For −1 < α < 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the [[lambda transition]] from a normal state to the [[superfluid]] state, for which experiments have found {{mvar|α}} = -0.013±0.003.At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample.This experimental value of α agrees with theoretical predictions based on variational perturbation theory. − For −1 < α < 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the lambda transition from a normal state to the superfluid state, for which experiments have found = -0.013±0.003.At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample. This experimental value of α agrees with theoretical predictions based on variational perturbation theory.+ − 当-1 <α<0时，热容在相变温度下具有“扭结”性质。这是'''<font color="#ff8000">液氦liquid helium</font>'''从正常状态到超流体状态的λ相变行为，在此实验中发现α= -0.013±0.003。为最小化样品中的压力差，至少有一次实验在轨道卫星的零重力条件下进行。α的这个实验值与基于'''<font color="#ff8000">变分微扰理论variational perturbation theory</font>'''的预测值相符。 − + − − For 0 < {{mvar|α}} < 1, the heat capacity diverges at the transition temperature (though, since {{mvar|α}} < 1, the enthalpy stays finite). An example of such behavior is the 3D ferromagnetic phase transition. In the three-dimensional [[Ising model]] for uniaxial magnets, detailed theoretical studies have yielded the exponent {{mvar|α}} ∼ +0.110. − − For 0 < < 1, the heat capacity diverges at the transition temperature (though, since < 1, the enthalpy stays finite). An example of such behavior is the 3D ferromagnetic phase transition. In the three-dimensional Ising model for uniaxial magnets, detailed theoretical studies have yielded the exponent ∼ +0.110. − − 当0 <α<1时，热容在相变温度处发散（也因为α<1，所以焓保持有限）。例如'''<font color="#ff8000">3D铁磁相变 3D ferromagnetic phase transition</font>'''。运用'''<font color="#ff8000">单轴磁体uniaxial magnets</font>'''的'''<font color="#ff8000">三维伊辛模型three-dimensional Ising model</font>'''，研究人员通过详细的理论研究得出指数α≈+0.110。 − − − − Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a [[logarithm]]ic divergence. However, these systems are limiting cases and an exception to the rule. Real phase transitions exhibit power-law behavior. − − Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a logarithmic divergence. However, these systems are limiting cases and an exception to the rule. Real phase transitions exhibit power-law behavior. − − 当然，存在一些不遵循幂律行为的模型系统。例如，平均场理论预测了相变温度下热容量的有限不连续性，而'''<font color="#ff8000">二维伊辛模型two-dimensional lsing model</font>'''则具有对数散度。但是，这样的系统数量有限，是例外。实际上大多相变仍然表现出幂律行为。 第333行：
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→特征属性
人们曾普遍认为，不管温度在临界温度之上还是临界温度之下，临界指数保持不变。但是现实证明这不一定正确：当连续对称属性因不相关的'''<font color="#ff8000">各向异性anisotropies</font>'''（在'''<font color="#ff8000">重整化群理论renormalization group</font>'''意义上）而分解为离散对称属性时，某些指数（例如<math>\gamma </math>，'''<font color="#ff8000"> 磁化率指数Exponent of the susceptibility</font>'''）会有所不同。
当<math>-1<α<0</math>时，热容在相变温度下具有“扭结”性质。这是'''<font color="#ff8000">液氦liquid helium</font>'''从正常状态到超流体状态的<math>\gamma </math>相变行为，在此实验中发现{{mvar|α}}= -0.013±0.003。为最小化样品中的压力差，至少有一次实验在轨道卫星的零重力条件下进行。α的这个实验值与基于'''<font color="#ff8000">变分微扰理论variational perturbation theory</font>'''的预测值相符。
当<math>0<α<1</math>时，热容在相变温度处发散（也因为<math>α<1</math>，所以焓保持有限）。例如'''<font color="#ff8000">3D铁磁相变 3D ferromagnetic phase transition</font>'''。运用'''<font color="#ff8000">单轴磁体uniaxial magnets</font>'''的'''<font color="#ff8000">三维[[伊辛模型]]three-dimensional Ising model</font>'''，研究人员通过详细的理论研究得出指数{{mvar|α}}≈+0.110。
当然，存在一些不遵循[[幂律]]行为的模型系统。例如，[[平均场理论]]预测了相变温度下热容量的有限不连续性，而'''<font color="#ff8000">二维[[伊辛模型]]two-dimensional lsing model</font>'''则具有对数散度。但是，这样的系统数量有限，是例外。实际上大多相变仍然表现出幂律行为。
在处于压力下的生物群中（接近临界转变时），相关性会增强，波动也会增加。许多以人、小鼠、树木和草类植物为研究对象的实验都得出了支持性的结果。
在处于压力下的生物群中（接近临界转变时），相关性会增强，波动也会增加。许多以人、小鼠、树木和草类植物为研究对象的实验都得出了支持性的结果。
== Experimental 实验性 ==
== Experimental 实验性 ==