The location of the Fisher zeros and estimates of y T = 1/ν are found for the Baxter–Wu model

Abstract

The Fisher zeros of the Baxter–Wu model are examined for the first time and for two series of finite-sized systems, with ‘spherical’ boundary conditions, their location is found to be extremely simple. They lie on the unit circle in the complex sinh[2βJ 3] plane. This is the same location as the Fisher zeros of the square lattice Ising model with nearest neighbour interactions and Brascamp–Kunz boundary conditions. The Baxter–Wu model is an Ising model with three-site interactions, J 3, on the triangle lattice. From the leading Fisher zeros, using finite-size scaling, accurate estimates of the critical exponent 1/ν are obtained and emphasis is placed on using different variables such as exp[−2βJ 3], exp[−4βJ 3], and sinh[2βJ 3] to enhance the accuracy of estimates. Furthermore, using the imaginary parts of the leading zeros versus the real part of the leading zeros, yields different results. This is similar to results of Janke and Kenna for the nearest neighbour, Ising model on the square lattice and extends this behaviour to a multisite interaction system in a different universality class than the pair-interaction cases.