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with a scaling function <math>G\ .</math>  Comparing this with ({{EquationNote|1=10}}), and recalling that the correlation length <math>\xi</math> diverges at the critical point as <math>t^{-\nu}</math> with exponent <math>\nu\ ,</math> we identify <math>p=-(d-2+\eta)</math> and <math>1/y=\nu\ .</math>  The scaling law <math>(2-\eta)\nu=\gamma\ ,</math> which was a consequence of the homogeneity of form of <math>h(r,t)\ ,</math> again holds, while from <math>1/y=\nu</math> and the earlier <math>d/y=2-\alpha</math> we now have the hyperscaling law ({{EquationNote|1=17}}), <math>d\nu=2-\alpha\ .</math>

with a scaling function <math>G\ .</math>  Comparing this with ({{EquationNote|1=10}}), and recalling that the correlation length <math>\xi</math> diverges at the critical point as <math>t^{-\nu}</math> with exponent <math>\nu\ ,</math> we identify <math>p=-(d-2+\eta)</math> and <math>1/y=\nu\ .</math>  The scaling law <math>(2-\eta)\nu=\gamma\ ,</math> which was a consequence of the homogeneity of form of <math>h(r,t)\ ,</math> again holds, while from <math>1/y=\nu</math> and the earlier <math>d/y=2-\alpha</math> we now have the hyperscaling law ({{EquationNote|1=17}}), <math>d\nu=2-\alpha\ .</math>

其中<math>G\ </math>是标度函数。与({{EquationNote|1=10}})对比，由临界点处的关联长度服从({{EquationNote|1=11}})，我们可得<math>p=-(d-2+\eta)</math>以及<math>1/y=\nu\ </math>。由此齐次性表达式<math>h(r,t)\ </math>得出的标度律<math>(2-\eta)\nu=\gamma\ </math>依然成立，且再由<math>1/y=\nu</math>和<math>d/y=2-\alpha</math>，得到超标度律({{EquationNote|1=17}})——<math>d\nu=2-\alpha\ </math>。

其中<math>G\ </math>是标度函数。与({{EquationNote|1=10}})对比，由临界点处的关联长度服从({{EquationNote|1=11}})，我们可得<math>p=-(d-2+\eta)</math>以及<math>1/y=\nu\ </math>。由此齐次性表达式<math>h(r,t)\ </math>得出的标度律<math>(2-\eta)\nu=\gamma\ </math>依然成立，且再由<math>1/y=\nu</math>和<math>d/y=2-\alpha</math>，得到超标度律({{EquationNote|1=17}})—<math>d\nu=2-\alpha\ </math>。

The block-spin picture thus yields the critical-point scaling of the thermodynamic and correlation functions, and both the <math>d</math>-independent and <math>d</math>-dependent relations among the scaling exponents. The essence of this picture is confirmed in the renormalization-group theory [19,20].

The block-spin picture thus yields the critical-point scaling of the thermodynamic and correlation functions, and both the <math>d</math>-independent and <math>d</math>-dependent relations among the scaling exponents. The essence of this picture is confirmed in the renormalization-group theory [19,20].

== References ==

== References ==