Honeycomb-lattice antiferromagnetic Ising model in a magnetic field

Abstract

The exact number of states Ω ( E , M ) of the Ising model only with the nearest-neighbor interaction J on L × 2 L honeycomb lattices (up to L = 12 ), as a function of energy E and magnetization M, is evaluated for the first time. For L = 12 , the total number of states is 2 288 ( ≈ 5 × 10 86 ). Classifying all states 2 288 according to their E and M values is an enormous work. Given the number of states Ω ( E , M ) , the exact partition function Z ( a , x ) = ∑ E , M Ω ( E , M ) a E x M is obtained, where a = e 2 β J ( β = 1 / k B T ) and x = e − 2 β H ( H: magnetic field). The properties of the honeycomb-lattice antiferromagnetic ( J < 0 ) Ising model in a magnetic field is discussed based on the exact partition function. The precise distributions of the partition function zeros in the complex temperature ( a = e 2 β J ) plane of the honeycomb-lattice Ising model for real H ≠ 0 are also obtained for the first time.