Partition function zeros at first-order phase transitions: Pirogov-Sinai theory
Abstract
This paper is a continuation of our previous analysis [BBCKK] of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of [BBCKK] were established are satisfied by a large class of lattice models. These models are characterized by two basic properties: The existence of only a finite number of ground states and the availability of an appropriate contour representation. This setting includes, for instance, the Ising, Potts and Blume-Capel models at low temperatures. The combined results of [BBCKK] and the present paper provide complete control of the zeros of the partition function with periodic boundary conditions for all models in the above class.
Cite
@article{arxiv.math-ph/0312041,
title = {Partition function zeros at first-order phase transitions: Pirogov-Sinai theory},
author = {Marek Biskup and Christian Borgs and Jennifer T. Chayes and Roman Kotecky},
journal= {arXiv preprint arXiv:math-ph/0312041},
year = {2007}
}
Comments
46 pages, 2 figs; continuation of math-ph/0304007 and math-ph/0004003, to appear in J. Statist. Phys. (special issue dedicated to Elliott Lieb)