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摘要翻译：
本文报道了关于简单正交晶格上三维Ising模型的猜想，并给出了精确解的计算细节。针对三维Ising模型的拓扑问题，提出了两个猜想，即第四卷曲维上的附加旋转和特征向量上的权因子作为边界条件。利用这些猜想，通过旋量分析计算了三维简单正交Ising模型的配分函数。根据猜想的正确性，简单正交Ising晶格的临界温度可以由kk*=kk′+kk′+kk′+k′k′′或sinh2k sinh2(k′+k′+k′k′/k)=1的关系确定。对于简单立方Ising晶格，根据K*=3k或Sinh2k，Sinh6k=1的结果，确定临界点精确地位于黄金分割比xc=exp(-2kc)=(sq(5)-1)/2处。如果猜想成立，则简单正交Ising系统的比热在相变临界点处将出现对数奇异性。导出了简单正交Ising铁磁体的自发磁化强度和自旋关联函数。简单正交Ising晶格的临界指数为:alpha=0,beta=3/8,gamma=5/4,delta=13/3,eta=1/8和nu=2/3,具有普适性，满足标度律。研究了临界点附近的合作现象，并与近似方法和实验结果进行了比较。3d到2d的交叉现象与2d到1d的交叉现象不同，指数从3d值到2d值有一个逐渐的交叉。
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英文标题：
《Conjectures on exact solution of three - dimensional (3D) simple
orthorhombic Ising lattices》
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作者：
Zhi-dong Zhang
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We report the conjectures on the three-dimensional (3D) Ising model on simple orthorhombic lattices, together with the details of calculations for a putative exact solution. Two conjectures, an additional rotation in the fourth curled-up dimension and the weight factors on the eigenvectors, are proposed to serve as a boundary condition to deal with the topologic problem of the 3D Ising model. The partition function of the 3D simple orthorhombic Ising model is evaluated by spinor analysis, by employing these conjectures. Based on the validity of the conjectures, the critical temperature of the simple orthorhombic Ising lattices could be determined by the relation of KK* = KK' + KK'' + K'K'' or sinh 2K sinh 2(K' + K'' + K'K''/K) = 1. For a simple cubic Ising lattice, the critical point is putatively determined to locate exactly at the golden ratio xc = exp(-2Kc) = (sq(5) - 1)/2, as derived from K* = 3K or sinh 2K sinh 6K = 1. If the conjectures would be true, the specific heat of the simple orthorhombic Ising system would show a logarithmic singularity at the critical point of the phase transition. The spontaneous magnetization and the spin correlation functions of the simple orthorhombic Ising ferromagnet are derived explicitly. The putative critical exponents derived explicitly for the simple orthorhombic Ising lattices are alpha = 0, beta = 3/8, gamma = 5/4, delta = 13/3, eta = 1/8 and nu = 2/3, showing the universality behavior and satisfying the scaling laws. The cooperative phenomena near the critical point are studied and the results obtained based on the conjectures are compared with those of the approximation methods and the experimental findings. The 3D to 2D crossover phenomenon differs with the 2D to 1D crossover phenomenon and there is a gradual crossover of the exponents from the 3D values to the 2D ones.
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PDF链接：
https://arxiv.org/pdf/705.1045
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