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We study the dynamics of a spin-flip model with a mean field interaction. Thesystem is non reversible, spacially inhomogeneous, and it is designed to modelsocial interactions. We obtain the limiting behavior of the empirical averagesin the limit of infinitely many interacting individuals, and show that phasetransition occurs. Then, after having obtained the dynamics of normalfluctuations around this limit, we analize long time fluctuations for criticalvalues of the parameters. We show that random inhomogeneities produce criticalfluctuations at a shorter time scale compared to the homogeneous system.

A simple mean field model for social interactions: dynamics, fluctuations, criticality