The role of disorder in the dynamics of critical fluctuations of mean field models

TL;DR

This paper investigates how disorder influences the critical fluctuation dynamics in mean field models like the Curie-Weiss and Kuramoto systems, revealing that disorder causes these models to belong to different universality classes at criticality.

Contribution

It provides a comparative analysis of the effects of disorder on critical fluctuations in two classical mean field models, highlighting a change in universality classes due to randomness.

Findings

Disorder causes Curie-Weiss and Kuramoto models to fall into different universality classes.

Critical fluctuations are significantly affected by the presence of disorder.

The models' limiting dynamics become deterministic with phase transitions as system size grows.

Abstract

The purpose of this paper is to analyze how the disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result concern the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).