Partition Function Zeros at First-Order Phase Transitions: Pirogov—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 ref. 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 ref. 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.