Lee-Yang Property and Gaussian multiplicative chaos

TL;DR

This paper investigates the Lee-Yang property in different spin models and Gaussian multiplicative chaos, showing it holds for some models but not for complex Gaussian chaos, based on distribution tail behavior.

Contribution

It establishes a connection between the Lee-Yang property and distribution tail behavior, demonstrating its validity in Ising and XY models but not in complex Gaussian chaos.

Findings

Lee-Yang property holds for Ising and XY models.

Lee-Yang property does not hold for complex Gaussian multiplicative chaos.

The proof links Lee-Yang property to distribution tail behavior.

Abstract

The Lee-Yang property of certain moment generating functions having only pure imaginary zeros is valid for Ising type models with one-component spins and XY models with two-component spins. Villain models and complex Gaussian multiplicative chaos are two-component systems analogous to XY models and related to Gaussian free fields. Although the Lee-Yang property is known to be valid generally in the first case, we show that is not so in the second. Our proof is based on two theorems of general interest relating the Lee-Yang property to distribution tail behavior.