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→Critical exponents 临界指数
=3</math> and (as noted above) <math>\alpha =0\ .</math>
=3</math> and (as noted above) <math>\alpha =0\ .</math>
({{EquationNote|8}})和({{EquationNote|9}})分别来自里斯和斯考特的贡献。它们大概是历史上最早版本的临界指数关系。在此之后，Domb和Sykes以及Fisher注意到指数<math>\gamma</math>实际上比平均场值<math>\gamma =1</math>大。而在更早之前，Guggenheim的对应状态分析就清楚地表明<math>\beta</math>值更靠近1/3而非平均场值的1/2.
({{EquationNote|8}})和({{EquationNote|9}})分别来自里斯和斯考特的贡献。它们大概是历史上最早版本的临界指数关系。在此之后，Domb和Sykes以及Fisher注意到指数<math>\gamma</math>实际上比平均场值<math>\gamma =1</math>大。而在更早之前，Guggenheim的对应状态分析就清楚地表明<math>\beta</math>值更靠近1/3而非平均场值的1/2。之后在<math>\gamma
=1</math>和<math>\beta \simeq 1/3\ ,</math>的假设下，里斯由({{EquationNote|8}})式总结出<math>\delta = 1+1/\beta
\simeq 4</math>（如今已知正确值接近5）。同时斯考特由({{EquationNote|9}})式得出<math>\alpha =1-2\beta \simeq 1/3</math>（正确值接近1/10）.另外平均场值<math>\delta
=3</math>，<math>\alpha =0\ </math>。
The long-range spatial correlation functions in ferromagnets and fluids also exhibit a homogeneity of form near the critical point. At magnetic field <math>H=0</math> (assumed for simplicity) the correlation function <math>h(r,t)</math> as a function of the spatial separation <math>r</math> (assumed very large) and temperature near the critical point (t assumed very small), is of the form [5,15]
The long-range spatial correlation functions in ferromagnets and fluids also exhibit a homogeneity of form near the critical point. At magnetic field <math>H=0</math> (assumed for simplicity) the correlation function <math>h(r,t)</math> as a function of the spatial separation <math>r</math> (assumed very large) and temperature near the critical point (t assumed very small), is of the form [5,15]