Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing
arXiv:2507.10406
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.
21 pages, 8 figures