Probing phase transition order of $q$-state Potts models using Wang-Landau Algorithm

TL;DR

This paper investigates the nature of phase transitions in the $q$-state Potts model with extra states using the Wang-Landau algorithm, identifying the critical point where the transition changes from second to first order.

Contribution

It applies the Wang-Landau method to analyze the phase transition order in the Potts model with additional states, providing insights into the critical value of $r$ for transition change.

Findings

Identified the critical value of $r$ for transition order change.

Demonstrated the effectiveness of DOSD in probing phase transition order.

Confirmed the transition change from second to first order at specific $r$.

Abstract

Phase transitions are ubiquitous phenomena, exemplified by the melting of ice and spontaneous magnetization of magnetic material. In general, a phase transition is associated with a symmetry breaking of a system; occurs due to the competition between coupling interaction and external fields such as thermal energy. If the phase transition occurs with no latent heat, the system experiences continuous transition, also known as second order phase transition. The ferromagnetic $q$-state Potts model with $r$ extra invisible states, introduced by Tamura, Tanaka, and Kawashima [Prog. Theor. Phys. 124, 381 (2010)], is studied by using the Wang-Landau method. The density of states difference (DOSD), $\ln g(E +\Delta E) - \ln g(E)$, is used to investigate the order of the phase transition and examine the critical value of $r$ changing the second to the first order transition.