# Universality of the third-order phase transition in the constrained Coulomb gas

## TL;DR

This paper demonstrates that the third-order phase transition in the free energy of constrained Coulomb gases is universal across dimensions and potential types, indicating a fundamental property of these systems.

## Contribution

It establishes the universality of the third-order phase transition in Coulomb gases across various dimensions and isotropic potentials.

## Key findings

- The phase transition is third-order in all dimensions.
- The transition behavior is largely independent of the specific potential.
- Universality suggests a fundamental characteristic of Coulomb gas systems.

## Abstract

The free energy at zero temperature of Coulomb gas systems in generic dimension is considered as a function of a volume constraint. The transition between the 'pulled' and the 'pushed' phases is characterised as a third-order phase transition, in all dimensions and for a rather large class of isotropic potentials. This suggests that the critical behaviour of the free energy at the 'pulled-to-pushed' transition may be universal, i.e., to some extent independent of the dimension and the details of the pairwise interaction.