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→Origin of homogeneity; block spins 齐次性的成因与块自旋
h(r,t) \equiv
h(r,t) \equiv
L^{p}h(r/L,L^yt); </math>
L^{p}h(r/L,L^yt); </math>
{{NumBlk|1=:|2=<math>h(r,t) \equiv
在重标度模型中，<math>t</math>变为<math>L^yt\ </math>，<math>r</math>则为<math>r/L\ </math>。对于关联函数<math>h(r,t)\ </math>标度律({{EquationNote|1=10}})，也存在某一指数<math>p\ </math>使<math>L^p</math>成为联系原始模型和重标度模型的因子；所以有：{{NumBlk|1=:|2=<math>h(r,t) \equiv
L^{p}h(r/L,L^yt);</math>|3={{EquationRef|21}}}}
L^{p}h(r/L,L^yt);</math>|3={{EquationRef|21}}}}
:<math>\label{eq:22}
:<math>\label{eq:22}
h(r,t)\equiv r^p G(r/t^{-1/y}) </math>
h(r,t)\equiv r^p G(r/t^{-1/y}) </math>
{{NumBlk|1=:|2=<math>h(r,t)h(r,t)\equiv r^p G(r/t^{-1/y})</math>|3={{EquationRef|22}}}}
即<math>h(r,t)</math>是<math>r</math>和<math>t^{-1/y}\ </math>的<math>p</math>次齐次函数。再由齐次性表达式({{EquationNote|1=2}})有：{{NumBlk|1=:|2=<math>h(r,t)h(r,t)\equiv r^p G(r/t^{-1/y})</math>|3={{EquationRef|22}}}}
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>。
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].