Phase Diagram and Critical Behavior of the Spin-1 Baxter-Wu Model with a Crystal Field

TL;DR

This study investigates the phase diagram and critical behavior of the spin-1 Baxter-Wu model with a crystal field, revealing a multi-critical point and continuous variation of critical exponents, challenging previous finite-size results.

Contribution

We provide a comprehensive analysis using renormalization group, finite-size scaling, and conformal invariance, showing new insights into the model's phase structure and critical properties.

Findings

Phase diagram similar to dilute 4-states Potts model

Identification of a multi-critical point at finite crystal field

Critical exponents vary continuously along the transition line

Abstract

The phase diagram and critical behavior of the spin-1 Baxter-Wu model with a crystal field in two dimensions is explored by renormalization group, conventional finite-size scaling and conformal invariance techniques. We found that the phase diagram of this model is qualitatively the same as that of the dilute 4-states Potts model, presenting a multi-critical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. However, our results indicate that the critical exponents vary continuously along the second-order transition line, differently from the expected behavior of the dilute 4-states Potts model.