Origin of the approximate universality of distributions in equilibrium correlated systems

TL;DR

This paper explains why distributions of global quantities in various equilibrium correlated systems resemble those of the 2D-XY model's magnetization, revealing a generic link between different models near criticality.

Contribution

It introduces a perturbative approach to connect the order parameter fluctuations of the Ising model to the 2D-XY model, explaining the universality of distribution forms.

Findings

Distributions of global quantities are similar across different models.

Effective action describes order parameter fluctuations near phase transition.

A generic link between D-dimensional Ising and XY models is established.

Abstract

We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the 2D-XY model . This approach, developed for the Ising model, is based on previous numerical observations. We obtain an effective action using a perturbative method, which successfully describes the order parameter fluctuations near the phase transition. This leads to a direct link between the D-dimensional Ising model and the XY model in the same dimension, which appears to be a generic feature of many equilibrium critical systems and which is at the heart of the above observations.