Partition function zeros at first-order phase transitions: Pirogov-Sinai theory

TL;DR

This paper extends previous work on partition function zeros at first-order phase transitions, demonstrating that the results apply to a broad class of lattice models with finite ground states and contour representations, including Ising, Potts, and Blume-Capel models.

Contribution

It shows that the assumptions for analyzing partition function zeros are satisfied by many models, providing comprehensive control over zeros in these systems.

Findings

Partition function zeros are fully characterized for models with finite ground states.

Results apply to Ising, Potts, and Blume-Capel models at low temperatures.

The analysis confirms the applicability of Pirogov-Sinai theory to these models.

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.