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arXiv · 1808.04130

Unusual changeover in the transition nature of local-interaction Potts models

Nir Schreiber·Reuven Cohen·Simi Haber·Gideon Amir·Baruch Barzel
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Abstract

A combinatorial approach is used to study the critical behavior of a $q$-state Potts model with a round-the-face interaction. Using this approach it is shown that the model exhibits a first order transition for $q>3$. A second order transition is numerically detected for $q=2$. Based on these findings, it is deduced that for some two-dimensional ferromagnetic Potts models with completely local interaction, there is a changeover in the transition order at a critical integer $q_c\leq 3$. This stands in contrast to the standard two-spin interaction Potts model where the maximal integer value for which the transition is continuous is $q_c=4$. A lower bound on the first order critical temperature is additionally derived.

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Nir Schreiber, Reuven Cohen, Simi Haber, Gideon Amir, Baruch Barzel. 2018-08-13. Unusual changeover in the transition nature of local-interaction Potts models. https://doi.org/10.1103/physreve.100.052119

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