自对偶Potts模型的表面自由能和角自由能
Surface and corner free energies of the self-dual Potts model
摘要：
本文研究了$Q > 4$的各向异性自对偶$Q$态Potts模型的体自由能、垂直面自由能、水平面自由能和角自由能$f_b, f_s, f'_s, f_c$. $f_b$于1973年计算[1]。对于$Q<4$，1989年计算了$f_s, f'_s$ [2]。在这里，我们将最后一个计算扩展到$Q>4$，并发现与Vernier和Jacobsen（VJ）[3]在2012年针对各向同性情况所做的计算一致。这四种自由能都满足反转和转动关系。与一些合理的分析性假设一起，这些提供了一种不太严格但简单得多的确定$f_b, f_s, f'_s$的方法。它们还意味着，$f_c$是独立的各向异性，是一个功能，只有$Q$，在这方面，他们类似于相关的六顶点模型的序参量。因此，VJ对$f_c$的猜想应该适用于完全各向异性模型。
英文摘要：
We consider the bulk, vertical surface, horizontal surface and corner free energies $f_b, f_s, f'_s, f_c$ of the anisotropic self-dual $Q$-state Potts model for $Q > 4$. $f_b$ was calculated in 1973[1]. For $Q<4$, $f_s, f'_s$ were calculated in 1989[2]. Here we extend this last calculation to $Q>4$ and find agreement with the conjectures made in 2012 by Vernier and Jacobsen (VJ)[3] for the isotropic case. All these four free energies satisfy inversion and rotation relations. Together with some plausible analyticity assumptions, these provide a less rigorous, but much simpler, way of determining $f_b, f_s, f'_s$. They also imply that $f_c$ is independent of the anisotropy, being a function only of $Q$, in which respect they resemble the order parameters of the associated six-vertex model. Hence VJ's conjecture for $f_c$ should apply to the full anisotropic model.
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