Partition Function Zeros at First-Order Phase Transitions: Piorogov-Sinai Theory

This paper is a continuation of our previous analysis [2] 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 [2] 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 [2] 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.