Ordinary, extraordinary, and normal surface transitions: Extraordinary-normal equivalence and simple explanation of ||T-Tc||2- alpha singularities.
Ordinary, extraordinary, and normal surface transitions: Extraordinary-normal equivalence and simple explanation of ||T-Tc||2- alpha singularities.
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普通、异常和正常表面转变：异常-正常等价和 ||T-Tc||2- alpha 奇点的简单解释。
DOI：
10.1103/physrevb.50.3894
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发表时间：
1994
影响因子：
3.7
通讯作者：
H. W. Diehl
中科院分区：
文献类型：
--
作者：
Theodore W. Burkhardt;H. W. Diehl
用简单、精确的方法证明了半无限d维Ising系统在异常跃迁和正常跃迁时的表面磁化强度m1和在正常跃迁、异常跃迁和正常跃迁时的表面能量密度ε 1具有主导热奇异性B_pm|不|^{2-\alpha}$，具有与体自由能$f_B（t，0）$相同的临界指数和振幅比。推导过程分三步进行：（i）通过追踪表面自旋，将具有超临界表面增强和表面磁场消失的半无限Ising模型精确地映射到具有亚临界表面增强、非零表面场和无关附加表面相互作用的半无限Ising模型上。这就建立了异常（$h_1=0，g>0$）和正常（$h_1\neq 0，g 0$）的等价性，只证明了与$f_B（t，0）-f_B（t，h）$成正比。(iii)在半空间z>0$和z<0$中温度为t +$和t$且无磁场的无限大系统界面处的能量密度ε 1 $与f B（t，0）-f B（t+，0）$成正比.
With simple, exact arguments we show that the surface magnetization $m_1$ at the extraordinary and normal transitions and the surface energy density $\epsilon_1$ at the ordinary, extraordinary, and normal transitions of semi-infinite $d$-dimensional Ising systems have leading thermal singularities $B_\pm |t|^{2-\alpha}$, with the same critical exponent and amplitude ratio as the bulk free energy $f_b(t,0)$. The derivation is carried out in three steps: (i) By tracing out the surface spins, the semi-infinite Ising model with supercritical surface enhancement $g$ and vanishing surface magnetic field $h_1$ is mapped exactly onto a semi-infinite Ising model with subcritical surface enhancement, a nonzero surface field, and irrelevant additional surface interactions. This establishes the equivalence of the extraordinary ($h_1=0, g>0$) and normal ($h_1\neq 0, g 0$ only is shown to be proportional to $f_b(t,0)-f_b(t,h)$. (iii) The energy density $\epsilon_1$ at the interface of an infinite system with temperatures $t_+$ and $t$ in the half-spaces $z>0$ and $z<0$ and no magnetic field is shown to be proportional to $f_b(t,0)-f_b(t_+,0)$.