Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing

TL;DR

This paper investigates a phase transition in particle systems driven by short-range repulsion and long-range attraction, enabling reversible switching between different states without hysteresis, with implications for understanding clustering and sorting phenomena.

Contribution

It introduces a universal expansion for vacuum bubble sizes and analyzes noise effects, providing new insights into phase transitions in particle systems.

Findings

Reversible switching between states achieved by infinitesimal parameter changes.

Universal expansion formula for vacuum bubble sizes.

Quantitative analysis of noise impact on phase transition.

Abstract

We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence of the transition, infinitesimal parameter variations allow switching between uniform distribution and clusters in single-species models, and between mixed and sorted states in multi-species contexts, without hysteresis. Our main technical contribution is a universal expansion for the size of vacuum bubbles that arise in this phase transition and a quantitative analysis of the effect of noise.