The High Temperature 2D Ising Model: The Lee-Yang Gap is the Mass Gap

Abstract

The Lee-Yang circle theorem applied to the two-dimensional Ising model asserts that the pressure observable is a meromorphic function of the external magnetic field whose singularities lie along the imaginary axis. These singularities have been extensively classified in the low-temperature regime using Pirogov-Sinai Theory. In the high-temperature phase, for fixed temperatures arbitrarily close to the critical temperature, we attempt to establish an asymptotic correspondence between the radius of analyticity of the pressure observable (the Lee-Yang gap), and the rate of exponential decay for two-point correlations (the mass gap). In addition this report presents an exposition to the high temperature 2D Ising model with a focus on mapping the regime of exponential decay for two-point correlations using the Lebowitz Penrose theorem.