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arXiv · 2507.10406

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

Arnd Scheel·Angela Stevens
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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.

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Arnd Scheel, Angela Stevens. 2025-07-14. Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing. https://arxiv.org/abs/2507.10406

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