Fluctuations in the two-dimensional one-component plasma and associated fourth-order phase transition

TL;DR

This paper analyzes the fluctuations of a 2D one-component plasma, revealing a fourth-order phase transition linked to a topological change in the plasma distribution, with implications for related integrable models.

Contribution

It explicitly computes large deviation functions for the plasma, identifying a novel fourth-order phase transition at the ground state, and connects these findings to Dyson Brownian motion and matrix models.

Findings

Identification of a fourth-order phase transition in 2D plasma fluctuations

Explicit large deviation functions for the radial displacement distribution

Connection to Dyson Brownian motion and non-Hermitian matrix models

Abstract

We study the distribution of the mean radial displacement of charges of a 2D one-component plasma in the thermodynamic limit $N\to\infty$ at finite temperature $\beta>0$. We compute explicitly the large deviation functions showing the emergence of a fourth-order phase transition as a consequence of a change of topology in the plasma distribution. This weak phase transition occurs exactly at the ground state of the plasma. These results have been compared with the integrable case (finite $N$) of plasma parameter $\beta q^2=2$. In this case the problem can be mapped to the stationary properties of 2D Dyson Brownian particles and to a non-Hermitian matrix model.