Critical properties of the eight-vertex model in a field

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.

arXiv comment7 pages, 10 figures

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• Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully non-universal
• Full nonuniversality of the symmetric 16-vertex model on the square lattice