Asymptotic correlation functions of Coulomb gases on an annulus

TL;DR

This paper analyzes the asymptotic behavior of correlation functions in two-dimensional Coulomb gases on an annulus at a specific inverse temperature, revealing universal and non-universal behaviors depending on symmetry.

Contribution

It applies orthogonal polynomial methods from random matrix theory to derive determinant forms and asymptotics of correlation functions for Coulomb gases on an annulus.

Findings

Correlation functions are expressed in determinant forms.

Universal behavior observed in systems with continuous rotational symmetry.

Breakdown of universality occurs in systems with discrete rotational symmetry.

Abstract

Two-dimensional Coulomb gases on an annulus at a special inverse temperature $\beta = 2$ are studied by using the orthogonal polynomial method borrowed from the theory of random matrices. The correlation functions among the Coulomb gas molecules are written in determinant forms and their asymptotic forms in the thermodynamic limit are evaluated. When the Coulomb gas system has a continuous rotational symmetry, the corresponding orthogonal polynomials are monomials, and one can see a universal behavior of the correlation functions in a thin annulus limit. In a system with a discrete rotational symmetry, the corresponding orthogonal polynomials are not in general monomials, and a breakdown of the universality is observed.