Critical and off-critical studies of the Baxter-Wu model with general toroidal boundary conditions

TL;DR

This paper analytically and numerically investigates the Baxter-Wu model with general toroidal boundary conditions, focusing on its operator content, eigenspectra, and conformal invariance near criticality.

Contribution

It extends the Bethe-ansatz solution to calculate eigenspectra and explores conformal invariance to determine mass ratios near the critical point.

Findings

Calculated operator content analytically and numerically.

Extended Bethe-ansatz solution for eigenspectra.

Determined mass ratios using conformal invariance.

Abstract

The operator content of the Baxter-Wu model with general toroidal boundary conditions is calculated analytically and numerically. These calculations were done by relating the partition function of the model with the generating function of a site-colouring problem in a hexagonal lattice. Extending the original Bethe-ansatz solution of the related colouring problem we are able to calculate the eigenspectra of both models by solving the associated Bethe-ansatz equations. We have also calculated, by exploring the conformal invariance at the critical point, the mass ratios of the underlying massive theory governing the Baxter-Wu model in the vicinity of its critical point.