Anomalous critical exponents in the anisotropic Ashkin-Teller model

TL;DR

This paper rigorously analyzes the Ashkin-Teller model's specific heat, revealing how universality transitions to nonuniversality and identifying new anomalous exponents that vary with interaction strength and anisotropy.

Contribution

It provides a rigorous computation of the specific heat and uncovers novel anomalous critical exponents in the anisotropic Ashkin-Teller model.

Findings

Identification of anomalous critical exponents

Demonstration of universality-nonuniversality crossover

Prediction of a new anomalous exponent varying with interaction

Abstract

We perform a rigorous computation of the specific heat of the Ashkin-Teller model in the case of small interaction and we explain how the universality-nonuniversality crossover is realized when the isotropic limit is reached. We prove that, even in the region where universality for the specific heat holds, anomalous critical exponents appear: for instance we predict the existence of a previously unknown anomalous exponent, continuously varying with the strength of the interaction, describing how the difference between the critical temperatures rescales with the anisotropy parameter.