General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions

TL;DR

This paper develops a comprehensive theory for Lee-Yang zeros in models with first-order phase transitions, revealing their complex geometric structures and providing formulas for their positions and densities.

Contribution

It introduces a rigorous, general framework for analyzing Lee-Yang zeros in models with first-order transitions, including non-symmetric cases and complex zero distributions.

Findings

Zeros lie on non-circular, topologically complex curves

Formulas for zero positions and densities are derived

Illustrated with Ising, Blume-Capel, and Potts models

Abstract

We present a general, rigorous theory of Lee-Yang zeros for models with first-order phase transitions that admit convergent contour expansions. We derive formulas for the positions and the density of the zeros. In particular, we show that for models without symmetry, the curves on which the zeros lie are generically not circles, and can have topologically nontrivial features, such as bifurcation. Our results are illustrated in three models in a complex field: the low-temperature Ising and Blume-Capel models, and the $q$-state Potts model for $q$ large enough.