Journal of Statistical Physics

, Volume 139, Issue 5, pp 820–858 | Cite as

A Simple Mean Field Model for Social Interactions: Dynamics, Fluctuations, Criticality

  • Francesca Collet
  • Paolo Dai Pra
  • Elena Sartori


We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in the limit of infinitely many interacting individuals, and show that phase transition occurs. Then, after having obtained the dynamics of normal fluctuations around this limit, we analyze long time fluctuations for critical values of the parameters. We show that random inhomogeneities produce critical fluctuations at a shorter time scale compared to the homogeneous system.


Critical dynamics Disordered model Fluctuations Interacting particle systems Large deviations Mean field interaction Non reversible Markov processes Phase transition Social interactions 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Francesca Collet
    • 1
  • Paolo Dai Pra
    • 1
  • Elena Sartori
    • 1
  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversity of PadovaPadovaItaly

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