The Brownian Mean Field model

Abstract

We discuss the dynamics and thermodynamics of the Brownian Mean Field (BMF) model which is a system of N Brownian particles moving on a circle and interacting via a cosine potential. It can be viewed as the canonical version of the Hamiltonian Mean Field (HMF) model. We first complete the description of this system in the mean field approximation. Then, we take fluctuations into account and study the stochastic evolution of the magnetization both in the homogeneous phase and in the inhomogeneous phase. We discuss its behavior close to the critical point.

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