Conformal invariance studies of the Baxter-Wu model and a related site-colouring problem

TL;DR

This paper explores the conformal invariance and finite-size scaling of the Baxter-Wu model and a related site-colouring problem, extending Bethe ansatz solutions to analyze their eigenspectra under various boundary conditions.

Contribution

It extends the Bethe ansatz solution to obtain eigenspectra for the Baxter-Wu model and related problems in finite geometries and toroidal boundary conditions.

Findings

Eigenspectra computed for large lattices.

Finite-size scaling corrections analyzed.

Conformal invariance properties studied.

Abstract

The partition function of the Baxter-Wu model is exactly related to the generating function of a site-colouring problem on a hexagonal lattice. We extend the original Bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions. The operator content of these models are studied by solving numerically the Bethe-ansatz equations and by exploring conformal invariance. Since the eigenspectra are calculated for large lattices, the corrections to finite-size scaling are also calculated.