Partition function zeros of the honeycomb-lattice Ising antiferromagnet in the complex magnetic-field plane

Abstract

The microcanonical transfer matrix is used to evaluate the exact integer values for the number of states Ω(E,M), as a function of energy E and magnetization M, of the Ising model in an external magnetic field H on L×2L honeycomb lattices (L=6,8,…,14) and (due to memory limitations) the exact real values for Ω(a,M)=∑(E)Ω(E,M)a(E) (L=16,…,22) , where a=e(2βJ). Given Ω(E,M) or Ω(a,M) , the exact partition functions Z(a,x)=∑(E,M)Ω(E,M)a(E)x(M)=∑(M)Ω(a,M)x(M), where x=e(-2βH), are obtained. From the exact partition functions, the precise distributions of the partition function zeros in the complex x plane of the honeycomb-lattice Ising antiferromagnet in a uniform external magnetic field, where the famous circle theorem for the partition function zeros of the Ising ferromagnet is not applicable, are determined. In addition, the critical points x(cp)(a) and the magnetic scaling exponents y(h)(a) of the honeycomb-lattice Ising antiferromagnet in a uniform magnetic field are estimated using its partition function zeros in the complex x plane. Our results for the critical points are also compared to those of the two different closed-form approximations.