Distribution of Yang-Lee Zeros of the ±JIsing Model

Abstract

A numerical technique to find out the distribution of the zeros of the partition function in the complex field plane is presented for the lsing model with arbitrary nearest-neighbor interactions. We apply it to the symmetric ± J model in two and three dimensions and obtain the distribution of the zeros of the effective partition function whose zeros in the complex field plane determine the analytical properties of the configuration-averaged free energy. Making use of the results, we discuss some problems of the short-range spin glass model including the existence of the Griffiths singularity and the AT line.