On the microcanonical solution of a system of fully coupled particles

We study the Hamiltonian mean field (HMF) model, a system of N fully couple d particles, in the microcanonical ensemble. We use the previously obtained free energy in the canonical ensemble to derive entropy as a function of e nergy, using Legendre transform techniques. The temperature-energy relation is found to coincide with the one obtained in the canonical ensemble and i ncludes a metastable branch which represents spatially homogeneous states b elow the critical energy. "Water bag" states, with removed tails momentum d istribution, lying on this branch, are shown to relax to equilibrium on a t ime which diverges linearly with N in an energy region just below the phase transition. (C) 2001 Elsevier Science Ltd. All rights reserved.