Phase transitions in self-dual generalizations of the Baxter-Wu model

TL;DR

This paper investigates two self-dual generalizations of the Baxter-Wu model using transfer-matrix and Monte Carlo methods, confirming phase transitions at self-dual points that appear to be discontinuous.

Contribution

It introduces two new self-dual generalizations of the Baxter-Wu model and analyzes their phase transition properties using numerical techniques.

Findings

Phase transitions occur at self-dual points.

Transitions are likely discontinuous.

Numerical methods confirm theoretical predictions.

Abstract

We study two types of generalized Baxter-Wu models, by means of transfer-matrix and Monte Carlo techniques. The first generalization allows for different couplings in the up- and down triangles, and the second generalization is to a $q$-state spin model with three-spin interactions. Both generalizations lead to self-dual models, so that the probable locations of the phase transitions follow. Our numerical analysis confirms that phase transitions occur at the self-dual points. For both generalizations of the Baxter-Wu model, the phase transitions appear to be discontinuous.