Equivalent-neighbor Potts models in two dimensions

TL;DR

This study uses Monte Carlo simulations to explore how the phase transition nature in two-dimensional Potts models with variable interaction ranges shifts from continuous to discontinuous as the number of equivalent neighbors increases, identifying critical points and fixed points.

Contribution

It provides the first detailed analysis of the transition from continuous to discontinuous phase transitions in 2D Potts models with variable interaction ranges, including locating tricritical points and fixed points.

Findings

Transitions are continuous for small z, fitting short-range universality classes.

Transitions become discontinuous at larger z, with specific thresholds identified.

The z=16 case for q=4 approximates the merged critical-tricritical fixed point.

Abstract

We investigate the two-dimensional $q=3$ and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number $z$ of equivalent neighbors. For not too large $z$, the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges the transitions become discontinuous. For $q=3$ we locate a tricritical point separating the continuous and discontinuous transitions near $z=80$, and a critical fixed point between $z=8$ and 12. For $q=4$ the transition becomes discontinuous for $z > 16$. The scaling behavior of the $q=4$ model with $z=16$ approximates that of the $q=4$ merged critical-tricritical fixed point predicted by the renormalization scenario.