临界指数

假设相变出现在临界温度T_c处。为研究临界温度附近物理量 f 的行为，我们引入约化温度

${\displaystyle \tau$ :={\frac {T-T_{\mathrm {c} }}{T_{\mathrm {c} }}}}

相变即发生于约化温度为0时。于是，可以定义临界指数${\displaystyle k}$:

${\displaystyle k\,{\stackrel {\text{def}}{=}}\,\lim _{\tau \to 0}{\frac {\log |f(\tau )|}{\log |\tau |}}}$

相应的幂律关系为

${\displaystyle f(\tau )\propto \tau ^{k}\,,\quad \tau \approx 0}$

这代表了τ → 0时函数f(τ)的渐近行为。更加普遍地，我们有

${\displaystyle f(\tau )=A\tau ^{k}\left(1+b\tau ^{k_{1}}+\cdots \right)}$

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