Ferromagnetic Potts models with multisite interaction

Abstract

We study the $q$ states Potts model with four site interaction on the square lattice. Based on the asymptotic behaviour of lattice animals, it is argued that when $q\le 4$ the system exhibits a second-order phase transition, and when $q>4$ the transition is first order. The $q=4$ model is borderline. We find $1/\ln q$ to be an upper bound on $T_c$, the exact critical temperature. Using a low-temperature expansion, we show that $1/(\theta \ln q)$, where $\theta >1$ is a $q$-dependent geometrical term, is an improved upper bound on $T_c$. In fact, our findings support $T_c=1/(\theta \ln q)$. This expression is used to estimate the finite correlation length in first-order transition systems. These results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four-site interaction model using the Wang-Landau entropic sampling method for $q=3,4,5$. In particular, the $q=4$ model shows an ambiguous finite-size pseudocritical behaviour.

8 pages, 6 figures

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• Scaling Relations for Logarithmic Corrections
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Cited by in corpus (3)

• Large-scale Ising Emulation with Four-Body Interaction and All-to-All Connection
• Unusual changeover in the transition nature of local-interaction Potts models
• Changeover phenomenon in randomly colored Potts models