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→Origin of homogeneity; block spins 齐次性的成因与块自旋
f(L^yt,
f(L^yt,
L^xH) \equiv L^df(t,H); </math>
L^xH) \equiv L^df(t,H); </math>
每一个自旋块通过与相邻块的共同边界相互作用。在对应的重标度模型中可以将它们视作单独的自旋。每个块的大小都是有限的，因此其内部的自旋只对系统的自由能提供解析项。自由能密度（单位自旋自由能）中包含临界点奇点及其指数的部分源自于自旋块间的相互作用。设自由能密度为<math>f(t,H)\ ,</math>，它是温度（由<math>t=T/T_c-1</math>）和磁场强度<math>H\ .</math>的函数。{{NumBlk|1=:|2=<math>f(L^yt,
每一个自旋块通过与相邻块的共同边界相互作用。在对应的重标度模型中可以将它们视作单独的自旋。每个块的大小都是有限的，因此其内部的自旋只对系统的自由能提供解析项。自由能密度（单位自旋自由能）中包含临界点奇点及其指数的部分源自于自旋块间的相互作用。设自由能密度为<math>f(t,H)\ ,</math>，它是温度（由<math>t=T/T_c-1</math>）和磁场强度<math>H\ .</math>的函数。在重标度后的图像中，相关长度与原始图像中相同，但以格子间距的数量来度量，前者比后者小<math>L\ </math>倍。因此，重标度模型实际上比原始模型离临界点更远。当逼近临界点时，<math>H</math>和<math>t</math>趋近于0，重标度模型中的有效<math>H</math>和<math>t</math>为<math>L^xH</math>和<math>L^yt</math>，其中<math>x</math>和<math>y\ ,</math>是正指数。从原始模型的角度来看，每个块的自旋对自由能奇异部分的贡献是<math>L^df(t,H)\ </math>，而对重标度模型来说，则是<math>f(L^yt, L^xH)\ </math>。因此有：{{NumBlk|1=:|2=<math>f(L^yt,
L^xH) \equiv L^df(t,H);</math>|3={{EquationRef|20}}}}
L^xH) \equiv L^df(t,H);</math>|3={{EquationRef|20}}}}
i.e., by ({{EquationNote|1=1}}), <math>f(t,H)</math> is a homogeneous function of <math>t</math> and <math>H^{y/x}</math> of degree <math>d/y\ .</math>
由({{EquationNote|1=1}})可得，<math>f(t,H)</math>是<math>t</math>和<math>H^{y/x}</math>的<math>d/y\ </math>次齐次函数。
Therefore, by ({{EquationNote|1=2}}), <math>f(t,H)=t^{d/y}
Therefore, by ({{EquationNote|1=2}}), <math>f(t,H)=t^{d/y}
f/\partial H)_T</math> the magnetization per spin, the homogeneity of form of <math>f(t,H)</math> in ({{EquationNote|1=20}}) is equivalent to that of <math>H(t,M)</math> in ({{EquationNote|1=7}}), from which the scaling laws <math>\gamma=\beta(\delta-1)</math> and <math>\alpha +
f/\partial H)_T</math> the magnetization per spin, the homogeneity of form of <math>f(t,H)</math> in ({{EquationNote|1=20}}) is equivalent to that of <math>H(t,M)</math> in ({{EquationNote|1=7}}), from which the scaling laws <math>\gamma=\beta(\delta-1)</math> and <math>\alpha +
2\beta + \gamma =2</math> are known to follow.
2\beta + \gamma =2</math> are known to follow.
因此，由({{EquationNote|1=2}})得<math>f(t,H)=t^{d/y}
\phi(H^{y/x}/t)=H^{d/x}\psi(t/H^{y/x})</math>，其中<math>\phi</math>和<math>\psi</math>仅仅是<math>H^{y/x}/t\ </math>的函数。
A related argument yields the scaling law ({{EquationNote|1=10}}) for the correlation function <math>h(r,t)\ ,</math> with <math>H=0</math> again for simplicity. In the re-scaled model, <math>t</math> becomes <math>L^yt\ ,</math> as before, while <math>r</math> becomes <math>r/L\ .</math> There may also be a factor, say <math>L^p</math> with some exponent <math>p\ ,</math> relating the magnitudes of the original and rescaled functions; thus,
A related argument yields the scaling law ({{EquationNote|1=10}}) for the correlation function <math>h(r,t)\ ,</math> with <math>H=0</math> again for simplicity. In the re-scaled model, <math>t</math> becomes <math>L^yt\ ,</math> as before, while <math>r</math> becomes <math>r/L\ .</math> There may also be a factor, say <math>L^p</math> with some exponent <math>p\ ,</math> relating the magnitudes of the original and rescaled functions; thus,