Phase Transition in Potts Model with Invisible States

TL;DR

This paper investigates how adding invisible states to the Potts model influences phase transition order, revealing a shift from second-order to first-order transitions due to entropy effects.

Contribution

It introduces a modified Potts model with invisible states and demonstrates that these states induce a first-order phase transition, unlike the second-order transition in the standard model.

Findings

Invisible states increase entropy without affecting internal energy.

The model exhibits a first-order phase transition with symmetry breaking.

Standard Potts model on 2D lattice shows second-order transition for q=2,3,4.

Abstract

We study phase transition in the ferromagnetic Potts model with invisible states that are added as redundant states by mean-field calculation and Monte Carlo simulation. Invisible states affect the entropy and the free energy, although they do not contribute to the internal energy. The internal energy and the number of degenerated ground states do not change, if invisible states are introduced into the standard Potts model. A second-order phase transition takes place at finite temperature in the standard $q$-state ferromagnetic Potts model on two-dimensional lattice for $q=2,3$, and 4. However, our present model on two-dimensional lattice undergoes a first-order phase transition with spontaneous $q$-fold symmetry breaking ($q=2,3$, and 4) due to entropy effect of invisible states. We believe that our present model is a fundamental model for analysis of a first-order phase transition with spontaneous discrete symmetry breaking.