Topological origin of the phase transition in a mean-field model
Statistical Mechanics
2009-10-31 v2
Abstract
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological transition occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N. Furthermore, as in statistical mechanics, also in topology the way the thermodynamic limit is taken is crucial.
Cite
@article{arxiv.cond-mat/9810406,
title = {Topological origin of the phase transition in a mean-field model},
author = {Lapo Casetti and E. G. D. Cohen and Marco Pettini},
journal= {arXiv preprint arXiv:cond-mat/9810406},
year = {2009}
}
Comments
REVTeX, 5 pages, with 1 eps figure included. Some changes in the text. To appear in Physical Review Letters