Thermodynamic limit of the first Lee‐Yang zero

Abstract

AbstractWe complete the verification of the 1952 Yang and Lee proposal that thermodynamic singularities are exactly the limits in of finite‐volume singularities in . For the Ising model defined on a finite at inverse temperature and external field h, let be the modulus of the first zero (that closest to the origin) of its partition function (in the variable h). We prove that decreases to as Λ increases to where is the radius of the largest disk centered at the origin in which the free energy in the thermodynamic limit is analytic. We also note that is strictly positive if and only if β is strictly less than the critical inverse temperature.