Non-Universal Critical Behaviour of Two-Dimensional Ising Systems

TL;DR

This paper identifies conditions under which two-dimensional Ising systems exhibit non-universal critical behavior, applicable to various models including the eight-vertex and Ashkin-Teller models, regardless of symmetry or interaction range.

Contribution

It establishes specific criteria for non-universal critical behavior in 2D Ising models, expanding understanding beyond traditional universality classes.

Findings

Conditions for non-universal critical behavior are derived.

Applicable to models with various symmetries and interaction ranges.

Includes models without translational or rotational invariance.

Abstract

Two conditions are derived for Ising models to show non-universal critical behaviour, namely conditions concerning 1) logarithmic singularity of the specific heat and 2) degeneracy of the ground state. These conditions are satisfied with the eight-vertex model, the Ashkin-Teller model, some Ising models with short- or long-range interactions and even Ising systems without the translational or the rotational invariance.