# Repulsion in low temperature $\beta$-ensembles

## TL;DR

This paper proves particle separation in a 2D Coulomb plasma at inverse temperatures greater than 1, showing that for large $eta$, particles are separated at the scale of the conjectured Abrikosov lattice.

## Contribution

It establishes a new result on particle separation in Coulomb plasmas for $eta>1$, connecting to the conjectural Abrikosov lattice structure.

## Key findings

- Particle separation occurs for $eta>1$
- Separation scale matches Abrikosov lattice conjecture at large $eta$
- Provides mathematical proof for particle distribution in Coulomb systems

## Abstract

We prove a result on separation of particles in a two-dimensional Coulomb plasma, which holds provided that the inverse temperature $\beta$ satisfies $\beta>1$. For large $\beta$, separation is obtained at the same scale as the conjectural Abrikosov lattice optimal separation.