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

TL;DR

This paper analyzes the short-time behavior of finite-size mean-field systems with non-conserved order parameters, deriving explicit expressions for early dynamics near critical points and confirming the short-time scaling hypothesis.

Contribution

It provides closed-form solutions for the initial moments of the order parameter in mean-field models, validating the short-time dynamical scaling hypothesis.

Findings

Confirmed validity of short-time scaling near critical points

Derived explicit expressions for early moments of the order parameter

Results extend to generic models with a single order parameter

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.