Critical properties of the eight-vertex model in a field

TL;DR

This paper uses numerical methods to analyze the critical properties of the eight-vertex model in a field, confirming theoretical predictions about universality classes and critical exponents.

Contribution

It provides numerical verification of the eight-vertex model's critical behavior in external fields, supporting the conjecture about universality class changes.

Findings

Critical exponents agree with Baxter's exact solution in zero-field case.

The model falls into the Ising universality class in a field, except for specific field combinations.

Weak universality persists in certain field configurations.

Abstract

The general eight-vertex model on a square lattice is studied numerically by using the Corner Transfer Matrix Renormalization Group method. The method is tested on the symmetric (zero-field) version of the model, the obtained dependence of critical exponents on model's parameters is in agreement with Baxter's exact solution and weak universality is verified with a high accuracy. It was suggested longtime ago that the symmetric eight-vertex model is a special exceptional case and in the presence of external fields the eight-vertex model falls into the Ising universality class. We confirm numerically this conjecture in a subspace of vertex weights, except for two specific combinations of vertical and horizontal fields for which the system still exhibits weak universality.