Universality of the weak pushed-to-pulled transition in systems with repulsive interactions

TL;DR

This paper demonstrates that a broad class of systems with repulsive interactions undergo a universal third-order phase transition between pushed and pulled phases, characterized by a specific free energy singularity.

Contribution

It establishes the universality of the pushed-to-pulled transition in systems with pairwise repulsive interactions, regardless of interaction range, dimension, or confinement details.

Findings

The excess free energy exhibits a universal third-order singularity.

The transition order parameter is the electrostatic pressure from surface excess charge.

The free energy expression interpolates between Coulomb and delta interactions.

Abstract

We consider a $d$-dimensional gas in canonical equilibrium under pairwise screened Coulomb repulsion and external confinement, and subject to a volume constraint. We show that its excess free energy displays a generic third-order singularity separating the pushed and pulled phases, irrespective of range of the pairwise interaction, dimension and details of the confining potential. The explicit expression of the excess free energy is universal and interpolates between the Coulomb (long-range) and the delta (zero-range) interaction. The order parameter of this transition - the electrostatic pressure generated by the surface excess charge - is determined by invoking a fundamental energy conservation argument.