对arXiv的回应：1209.0731“三维（3D）简单正交伊辛晶格的错误解决方案”，Perk
Response to arXiv:1209.0731 'Erroneous solution of three-dimensional (3D) simple orthorhombic Ising lattices' by Perk
摘要：
本文是对J.H.H.教授的回应。Perk最近的评论（arXiv：1209.0731v1）.指出三维伊辛模型的约化自由能βf、单位自由能f和自由能F的奇异性在β = 0处不同.在Perk的评论中给出的严格证明仅仅是对约化自由能βf的解析性，它在β = 0时失去了定义。因此，他的所有反对意见都失去了数学基础，这些都被彻底推翻了。这意味着级数展开式不能作为判断三维伊辛模型精确解正确性的标准。此外，我们注意到，有没有评论的拓扑为基础的方法开发的张的精确解的三维伊辛模型。对J.H.H.教授的回答添加Perk在arXiv：1209.0731v2中的公开信。我们证明了硬核模型和伊辛模型在β中的解析性是在β > 0时得到的，而不是在β = 0时得到的.此外，单位点自由能f和折合自由能βf在β = 0时失去定义，因此它们中的任何一个在无限温度下的高温级数展开式中都有两种不同的形式。用于3D共形场论的三个独立维拉索罗代数可以写在3+1维空间内（即，3-球体）与权重因子。
英文摘要：
This paper is a Response to Professor J.H.H. Perk's recent Comment (arXiv:1209.0731v1). We point out that the singularities of the reduced free energy βf, the free energy per site f and the free energy F of the 3D Ising model differ at β = 0. The rigorous proof presented in the Perk's Comment is only for the analyticity of the reduced free energy βf, which loses its definition at β = 0. Therefore, all of his objections lose the mathematical basis, which are thoroughly disproved. This means that the series expansions cannot serve as a standard for judging the correctness of the exact solution of the 3D Ising model. Furthermore, we note that there have been no comments on the topology-based approach developed by Zhang for the exact solution of the 3D Ising model. A Rejoinder to Professor J.H.H. Perk's open letter in arXiv:1209.0731v2 is added. We show that the analyticity in β of both the hard-core and Ising models is proved for β > 0, not for β = 0. Furthermore, the free energy per site f and the reduced free energy βf lose their definitions at β = 0, and thus either of them could have two different forms for high-temperature series expansions at/below infinite temperature. Three independent Virasoro algebras for 3D conformal field theory can be written within the 3+1 dimensional space (i.e., 3-sphere) with weight factors.
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