596
个编辑
更改
跳到导航
跳到搜索
第203行：
第203行： − +
→Critical exponents 临界指数
Thus, as <math>r\rightarrow \infty</math> in any fixed thermodynamic state (fixed t) near the critical point, <math>h</math> decays with increasing <math>r</math> proportionally to <math>r^{-\frac{1}{2}(d-1)}e^{-r/\xi}\ ,</math> as in the [https://en.wikipedia.org/wiki/Ornstein%E2%80%93Zernike_equation?oldformat=true '''Ornstein-Zernike theory''']. If, instead, the critical point is approached <math>(\xi \rightarrow \infty)</math> with a fixed, large <math>r\ ,</math> we have <math>h(r)</math> decaying with <math>r</math> only as an inverse power, <math>r^{-(d-2+\eta)}\ ,</math> which corrects the <math>r^{-(d-2)}</math> that appears in the Ornstein-Zernike theory in that limit. The scaling law({{EquationNote|1=10}}) with scaling function <math>G(x)</math> interpolates between these extremes.
Thus, as <math>r\rightarrow \infty</math> in any fixed thermodynamic state (fixed t) near the critical point, <math>h</math> decays with increasing <math>r</math> proportionally to <math>r^{-\frac{1}{2}(d-1)}e^{-r/\xi}\ ,</math> as in the [https://en.wikipedia.org/wiki/Ornstein%E2%80%93Zernike_equation?oldformat=true '''Ornstein-Zernike theory''']. If, instead, the critical point is approached <math>(\xi \rightarrow \infty)</math> with a fixed, large <math>r\ ,</math> we have <math>h(r)</math> decaying with <math>r</math> only as an inverse power, <math>r^{-(d-2+\eta)}\ ,</math> which corrects the <math>r^{-(d-2)}</math> that appears in the Ornstein-Zernike theory in that limit. The scaling law({{EquationNote|1=10}}) with scaling function <math>G(x)</math> interpolates between these extremes.
因此，在任何靠近临界点的恒温热力学状态下，当<math>r\rightarrow \infty</math>时，<math>h</math>随<math>r</math>的增加而衰减至<math>r^{-\frac{1}{2}(d-1)}e^{-r/\xi}\ </math>（参见'''[https://en.wikipedia.org/wiki/Ornstein%E2%80%93Zernike_equation? 奥恩斯泰因-泽尔尼克理论 Ornstein-Zernike theory]'''）
因此，在任何靠近临界点的恒温热力学状态下，当<math>r\rightarrow \infty</math>时，<math>h</math>随<math>r</math>的增加而衰减至<math>r^{-\frac{1}{2}(d-1)}e^{-r/\xi}\ </math>（参见'''[https://en.wikipedia.org/wiki/Ornstein%E2%80%93Zernike_equation? 奥恩斯泰因-泽尔尼克理论 Ornstein-Zernike theory]'''）。
In the language of fluids, with <math>\rho</math> the number density and <math>\chi</math> the isothermal compressibility, we have as an exact relation in the Ornstein-Zernike theory
In the language of fluids, with <math>\rho</math> the number density and <math>\chi</math> the isothermal compressibility, we have as an exact relation in the Ornstein-Zernike theory