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

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 $q_c\le 3$. 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.

arXiv comment8 pages, 3 figures

References in corpus (9)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Continuity of the phase transition for planar random-cluster and Potts models with $1\le q\le 4$
• Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$
• Microcanonical Approach to the Simulation of First-Order Phase Transitions
• Phase Transition in Potts Model with Invisible States
• First-Order Phase Transition in Potts Models with finite-range interactions
• Ferromagnetic Potts models with multisite interaction
• First-order transition in Potts models with "invisible' states: Rigorous proofs
• Scaling in the vicinity of the four-state Potts fixed point

Cited by in corpus (1)

• Changeover phenomenon in randomly colored Potts models