Short-time dynamics of finite-size mean-field systems

Abstract

We study the short-time dynamics of a mean-field model with non-conserved order parameter (Curie-Weiss with Glauber dynamics) by solving the associated Fokker-Planck equation. We obtain closed-form expressions for the first moments of the order parameter, near to both the critical and spinodal points, starting from different initial conditions. This allows us to confirm the validity of the short-time dynamical scaling hypothesis in both cases. Although the procedure is illustrated for a particular mean-field model, our results can be straightforwardly extended to generic models with a single order parameter.

accepted for publication in JSTAT

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• Contact geometric approach to Glauber dynamics near a cusp and its limitation
• Analysis of the finite-size effect of the long-range Ising model under Glauber dynamics
• Analysis of finite-size effect of infinite-range Ising model under Glauber dynamics