Criterion for universality class independent critical fluctuations: example of the 2D Ising model

TL;DR

This paper investigates order parameter fluctuations in the 2D Ising model near criticality, identifying specific loci where fluctuations resemble those of the 2D-XY model, suggesting a universal behavior independent of universality class.

Contribution

It introduces loci of temperature and magnetic field where fluctuation distributions are universal across different models, challenging the notion that fluctuations are solely class-dependent.

Findings

Fluctuation distributions along specific loci resemble 2D-XY model.

Maximum fluctuation range occurs along these loci, not at critical temperature.

Universality of fluctuations is independent of the model's universality class.

Abstract

Order parameter fluctuations for the two dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T*(L) and of magnetic fields B*(L) are identified, for which the probability density function is similar to that for the 2D-XY model in the spin wave approximation.The characteristics of the fluctuations along these points are largely independent of universality class. We show that the largest range of fluctuations relative to the variance of the distribution occurs along these loci of points, rather than at the critical temperature itself and we discuss this observation in terms of intermittency. Our motivation is the identification of a generic form for fluctuations in correlated systems in accordance with recent experimental and numerical observations. We conclude that a universality class dependent form for the fluctuations is a particularity of critical phenomena related to the change in symmetry at a phase transition.