Density of Zeros on the Lee-Yang Circle for Two Ising Ferromagnets

Abstract

Extrapolations of high-field and high-temperature series expansions have been used to construct numerical approximations to the density of zeros $g(\ensuremath{\theta})$ on the Lee-Yang circle for the Ising ferromagnets on a two-dimensional square and a three-dimensional diamond lattice. For temperatures above the critical temperature the density is zero for $|\ensuremath{\theta}|<{\ensuremath{\theta}}_{G}$ and then varies as ${(\ensuremath{\theta}\ensuremath{-}{\ensuremath{\theta}}_{G})}^{\ensuremath{\mu}}$, with $\ensuremath{\mu}\ensuremath{\simeq}\ensuremath{-}0.1 \mathrm{and} +0.1$ for the square and diamond lattices, respectively.