On the microcanonical solution of a system of globally coupled rotators
Abstract
We study the Hamiltonian Mean Field (HMF) model, a system of fully coupled particles, in the microcanonical ensemble. We use the previously obtained free energy in the canonical ensemble to derive entropy as a function of energy, using Legendre transform techniques. The temperature-energy relation is found to coincide with the one obtained in the canonical ensemble and includes a {\it metastable} branch which represents spatially homogeneous states below the critical energy. "Water bag" states, with removed tails momentum distribution, lying on this branch, are shown to relax to equilibrium on a time which diverges linearly with in an energy region just below the phase transition.
Keywords
Cite
@article{arxiv.cond-mat/9810048,
title = {On the microcanonical solution of a system of globally coupled rotators},
author = {Mickael Antoni and Haye Hinrichsen and Stefano Ruffo},
journal= {arXiv preprint arXiv:cond-mat/9810048},
year = {2007}
}
Comments
Invited paper to the Denton workshop (April 3-6, 2000). 5 LaTeX pages, 2 figures. To appear in a special issue of "Chaos, Solitons and Fractals"