回应arXiv：0811.1802“评论'关于三维（3D）伊辛晶格的精确解的猜想'”由Perk和奇点在/接近无限温度：回复Perk的答辩arXiv：0901.2935
Response to arXiv:0811.1802 "Comment on 'Conjectures on exact solution of three-dimensional (3D) Ising lattices'" by Perk and Singularities at/near infinite temperature: Reply to Perk's Rejoinder arXiv:0901.2935
摘要：
第一部分：方程组的误差。(15b)在我的文章[Z.D.张菲尔Mag. 87，5309（2007），arXiv：0705.1045]在应用Jordan-Wigner变换时，不影响假定精确解的有效性，因为解不是直接从它导出的。Perk的评论arXiv：0811.1802v2的其他反对意见与Wu等人的评论arXiv：0811.3876和arXiv：0812.2837中的反对意见相同，这些反对意见没有坚实的基础，并且在之前的回应arXiv：0812.2330中被拒绝。该解可以用来理解各种系统中的临界现象，而该解是开放的，可以严格证明。第二部分：这是对Perk的反驳arXiv：0901.2935的答复。它表明，在Perk的反驳的基础上的反对意见，相对于奇点在/接近无限的温度，是基于一个错误，混合的概念T接近无限和T =无限。它表明，单位点的约化自由能f只能用于有限的温度（β> 0），而不是“完全”无限的温度（β = 0）。在热力学极限N接近无穷大时，除了Z在z = -1处的无限温度零点之外，对于H = +/- i在β接近零的极限中无限大，配分函数在z = 1处存在另一个奇点，这通常在文献中通过将Z设置为1/N的幂并将总自由能F除以N（相等地，忽略1/Z的零点的奇异性。Perk的反驳中的反对意见被彻底推翻。
英文摘要：
Part I: The error of eq. (15b) in my article [Z.D. Zhang, Phil. Mag. 87, 5309 (2007), arXiv:0705.1045] in the application of the Jordan-Wigner transformation does not affect the validity of the putative exact solution, since the solution is not derived directly from it. Other objections of Perk's Comment arXiv:0811.1802v2 are the same as those in Wu et al's Comments arXiv:0811.3876 and arXiv:0812.2837, which do not stand on solid ground and have been rejected in the previous Response arXiv:0812.2330. The conjectured solution can be utilized to understand critical phenomena in various systems, while the conjectures are open to prove rigorously. Part II: This is a Reply to Perk's Rejoinder arXiv:0901.2935. It is shown that the basis of the objections in Perk's Rejoinder, with respect to singularities at/near infinite temperature, is based on an error that mixes the concepts of T approaching infinite and T = infinite. It is shown that the reduced free energy per site f can be used only for finite temperatures (beta > 0), not for 'exactly' infinite temperature (beta = 0). At the thermodynamic limit N approaches infinite, besides infinite-temperature zeros of Z at z = -1 for H = +/- i infinite in the limit of beta approaching zero, there exists another singularity at z = 1 for the partition function, which is usually concealed in literature by setting Z to the power of 1/N and dividing the total free energy F by N (equally, disregarding the singularity of zeros of 1/Z. The objections in Perk's Rejoinder are thoroughly disproved.
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