Universality in the two-dimensional dilute Baxter-Wu model

TL;DR

This study investigates the universality class of the phase transition in the two-dimensional spin-1 Baxter-Wu model with a crystal field, using extensive numerical simulations and finite-size scaling analysis.

Contribution

It provides new numerical evidence that the phase transition belongs to the 4-state Potts universality class, clarifying previous controversies.

Findings

Transition belongs to the 4-state Potts universality class.

Finite-size effects significantly influence the observed transition nature.

Strong finite-size effects are especially prominent near the pentacritical point.

Abstract

We study the question of universality in the two-dimensional spin-$1$ Baxter-Wu model in the presence of a crystal field $\Delta$. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of $\Delta$ and a parallelized variant of the multicanonical approach performed at constant temperature $T$. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the $(\Delta, T)$ phase diagram indicates that the transition belongs to the universality class of the $4$-state Potts model. Previous controversies with respect to the nature of the transition are discussed and possibly attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model.