  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).
