Critical lines of the Yang-Lee edge singularity of Ising ferromagnets on square, triangular, and honeycomb lattices

Abstract

We extend our previous approach to determine the critical lines of the Yang-Lee edge singularity of Ising ferromagnets on square, triangular, and honeycomb lattices by considering the zeros of the Ising partition function on elementary cycles of these lattices. It is found that the critical lines have the properties h(0)-->t(15/8) as T-->T-c + and beta h(0)-->pi/2 as T-->infinity. Using the asymptotic formulas valid in the high-temperature limit and the zero-field limit we obtain the functional form of the critical line.