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arXiv · 1712.07047

Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations

Jian-Ping Lv·Youjin Deng·Jesper Lykke Jacobsen·Jesús Salas·Alan D. Sokal
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Abstract

We provide a new criterion based on graph duality to predict whether the 3-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge $c=1$. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the 3-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

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Jian-Ping Lv, Youjin Deng, Jesper Lykke Jacobsen, Jesús Salas, Alan D. Sokal. 2018-05-04. Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations. https://doi.org/10.1103/physreve.97.040104

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