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arXiv · 1606.01616

Surface and corner free energies of the self-dual Potts model

R. J. Baxter
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Abstract

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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R. J. Baxter. 2016-06-06. Surface and corner free energies of the self-dual Potts model. https://arxiv.org/abs/1606.01616

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