Density of Yang–Lee zeros and Yang–Lee edge singularity for the antiferromagnetic Ising model

Abstract

The microcanonical transfer matrix is used to evaluate the exact partition function of the antiferromagnetic (AF) Ising model on L × L square lattices in an arbitrary nonzero external magnetic field at arbitrary temperature. The precise distribution of the Yang–Lee zeros in the complex x = e − 2 β H plane for the AF Ising model is determined as a function of temperature. Some of the Yang–Lee zeros for the AF Ising model lie on the negative real x axis, and the number of the zeros on the negative real axis is increased as temperature increases. The zeros on the negative real axis accumulate at their right end x e . In the thermodynamic limit ( L → ∞ ), the density of the zeros g ( x ) on the negative real axis of the AF Ising model diverges at x e for all temperatures. Therefore, the AF Ising model has the Yang–Lee edge singularity x e whose existence has been known in the ferromagnetic models only for T > T c . For the AF Ising model the density of zeros near x e is given by g ( x ) ∼ ( x − x e ) − 1 / 6 , in the same way for the ferromagnetic models.