Partition Function Zeros and Shift Exponent of the Ising Model on a Square Lattice with Self-dual Boundary Conditions

Abstract

The exact integer values for the density of states of the Ising model on an L×L square lattice with self-dual boundary conditions are evaluated up to L = 22 for the first time by counting all possible spin states (enormous 2485 ≈ 10146 states for L = 22). The exact partition function zeros in the complex temperature plane, very sensitive indicators for phase transitions and critical phenomena, are obtained by using the density of states. From the behavior of the partition function zeros, the shift exponent λ of the square-lattice Ising model with self-dual boundary conditions is accurately and precisely estimated to be λ = 2.0000000(2), clearly indicating λ = 2.