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

TL;DR

This study investigates the symmetric eight-vertex model on a square lattice in both electric and magnetic formats, revealing non-universality in the electric formulation through numerical and analytical methods.

Contribution

The paper introduces a comprehensive numerical and analytical analysis of the symmetric eight-vertex model, demonstrating its non-universality in the electric vertex formulation.

Findings

Numerical data confirms weak universality in the magnetic format.

Analytic formulas show electric exponents depend on model parameters.

Electric formulation exhibits full non-universality, unlike the magnetic format.

Abstract

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the Corner Transfer Matrix Renormalization Group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on model's parameters agree with Baxter's exact solution and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents $\eta$ and $\delta$ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents $\eta_{\rm e}$ and $\delta_{\rm e}$ which agree with our numerical data. These exponents depend on model's parameters which is an evidence for the full non-universality of the symmetric eight-vertex model in the original electric formulation.