Large Deviations of Radial Statistics in the Two-Dimensional One-Component Plasma

Abstract

The two-dimensional one-component plasma is an ubiquitous model for several vortex systems. For special values of the coupling constant βq2 (where q is the particles charge and β 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 βq2= 2.