The location of the Fisher zeros and estimates of yT = 1/{\nu} are found for the Baxter-Wu model

TL;DR

This paper investigates the Fisher zeros of the Baxter-Wu model, revealing their simple circular distribution and deriving estimates for the critical exponent using finite size scaling, extending known behaviors from the Ising model.

Contribution

It demonstrates that the Fisher zeros of the Baxter-Wu model lie on a simple circle and provides new estimates of the critical exponent using finite size scaling methods.

Findings

Fisher zeros lie on the unit circle in the complex plane.

Accurate estimates of the critical exponent 1/ν are obtained.

The behavior of zeros is similar to the Ising model with nearest neighbor interactions.

Abstract

It is shown that the location of the Fisher zeros of the Baxter-Wu model, for two series of finite sized clusters, with spherical boundary conditions, is extremely simple. They lie on the unit circle in the complex Sinh[2\b{eta}J3] plane. This is the same location as the Fisher zeros of the Ising model with nearest neighbor interactions, J2, on the square lattice have, with Brascamp-Kunz boundary conditions. The Baxter-Wu model is an Ising model with three site interactions, J3, on the triangle lattice. From the leading Fisher zeros, using finite size scaling, accurate estimates of the critical exponent 1/{\nu} are obtained. Furthermore, using the imaginary parts of the leading zeros versus the real part of the leading zeros leads to different results similar the results of Janke and Kenna for the nearest neighbor, Ising model on the square lattice and extending this behavior to a multi-site interaction system.