Large deviations of radial statistics in the two-dimensional one-component plasma

TL;DR

This paper investigates large deviation behaviors of radial observables in the 2D one-component plasma, revealing complex phase structures, split-off phenomena, and conditions where fluid assumptions break down, supported by analytical and numerical results.

Contribution

It provides explicit large deviation functions for radial observables in the 2D plasma, including next-to-leading order terms, and uncovers phenomena like split-off fluctuations and phase breakdowns.

Findings

Explicit large deviation functions including 1/N corrections.

Identification of split-off phenomena in edge density fluctuations.

Conditions under which fluid phase assumptions fail.

Abstract

The two-dimensional one-component plasma is an ubiquitous model for several vortex systems. For special values of the coupling constant $\beta q^2$ (where $q$ is the particles charge and $\beta$ the inverse temperature), the model also corresponds to the eigenvalues distribution of normal matrix models. Several features of the system are discussed in the limit of large number $N$ of particles for generic values of the coupling constant. We show that the statistics of a class of radial observables produces a rich phase diagram, and their asymptotic behaviour in terms of large deviation functions is calculated explicitly, including next-to-leading terms up to order 1/N. We demonstrate a split-off phenomenon associated to atypical fluctuations of the edge density profile. We also show explicitly that a failure of the fluid phase assumption of the plasma can break a genuine $1/N$-expansion of the free energy. Our findings are corroborated by numerical comparisons with exact finite-N formulae valid for $\beta q^2=2$.