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Abstract We consider simple mean field continuum models for first order liquid–liquid demixing and solid–liquid phase transitions and show how the Maxwell construction at phase coexistence emerges on going from finite-size closed systems to the thermodynamic limit. The theories considered are the Cahn–Hilliard model of phase separation, which is also a model for the liquid-gas transition, and the phase field crystal model of the solid–liquid transition. Our results show that states comprising the Maxwell line depend strongly on the mean density with spatially localized structures playing a key role in the approach to the thermodynamic limit.
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This content will become publicly available on April 2, 2026
Banded phases in topological flocks
Flocking phase transitions arise in many aligning active soft matter systems, and an interesting question concerns the role of “topological” vs. “metric” interactions on these transitions. While recent theoretical work suggests that the order–disorder transition in these polar aligning models is universally first order, numerical studies have suggested that topological models may instead have a continuous transition. Some recent simulations have found that some variations of topologically interacting flocking agents have a discontinuous transition, but unambiguous observations of phase coexistence using common Voronoi-based alignment remains elusive. In this work, we use a custom GPU-accelerated simulation package to perform million-particle-scale simulations of a Voronoi–Vicsek model in which alignment interactions stem from an XY-like Hamiltonian. By accessing such large systems on appropriately long time scales and in the time-continuous limit, we are able to show a regime of stable phase coexistence between the ordered and disordered phases, confirming the discontinuous nature of this transition in the thermodynamic limit.
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- Award ID(s):
- 2143815
- PAR ID:
- 10581475
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 21
- Issue:
- 14
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 2646 to 2653
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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