596
个编辑
更改
跳到导航
跳到搜索
第348行：
第348行： − + + +
→Origin of homogeneity; block spins 齐次性的成因与块自旋
因此，由({{EquationNote|1=2}})得<math>f(t,H)=t^{d/y}
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。当<math>H=0</math>，由第一个关系式可得<math>f(t,0)=\phi(0)t^{d/y}\ </math>。但是<math>f(t,0)</math>的两个温度导数对单位自旋热容有贡献，且以<math>t^{-\alpha}\ </math>发散，所以有<math>d/y=2-\alpha\ </math>。另外，在临界等温线<math>(t=0)\ </math>上，由第二个关系式可得<math>f(0,H)=\psi(0)H^{d/x}\ </math>。但单位自旋磁化强度<math>-(\partial f/\partial H)_T\ </math>随<math>H^{d/x-1}\ </math>衰减，因此<math>d/x-1=1/\delta\ </math>。
\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。当<math>H=0</math>，由第一个关系式可得<math>f(t,0)=\phi(0)t^{d/y}\ </math>。但是<math>f(t,0)</math>的两个温度导数对单位自旋热容有贡献，且以<math>t^{-\alpha}\ </math>发散，所以有<math>d/y=2-\alpha\ </math>。另外，在临界等温线<math>(t=0)\ </math>上，由第二个关系式可得<math>f(0,H)=\psi(0)H^{d/x}\ </math>。但单位自旋磁化强度<math>-(\partial f/\partial H)_T\ </math>随<math>H^{d/x-1}\ </math>衰减，因此<math>d/x-1=1/\delta\ </math>。指数<math>d/x</math>与<math>d/y</math>可以由热容指数<math>\alpha</math>和临界等温线指数<math>\delta\ </math>定义。同时再有单位自旋磁化强度<math>-(\partial
f/\partial H)_T</math>，({{EquationNote|1=20}})中<math>f(t,H)</math>的齐次形式与({{EquationNote|1=7}})式<math>H(t,M)</math>的齐次形式等价，由此得到标度律<math>\gamma=\beta(\delta-1)</math>和<math>\alpha +
2\beta + \gamma =2</math>。
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,