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

The purpose of this paper is to analyze how 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 concerns 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).