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  • Letter
  • Open Access

Phase separation with nonlocal interactions

Filipe C. Thewes, Yicheng Qiang, Oliver W. Paulin, and David Zwicker*

  • *Contact author: david.zwicker@ds.mpg.de
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Phys. Rev. Research 8, L022023 – Published 4 May, 2026

DOI: https://doi.org/10.1103/gdwt-v9yj

Abstract

Phase separation in complex systems is a ubiquitous phenomenon. While simple theories predict coarsening until only macroscopically large phases remain, concrete models often exhibit patterns with finite length scales. To unify such models, we here propose a general field-theoretic model that combines phase separation with nonlocal interactions. Our analysis reveals that long-range interactions generally suppress coarsening, whereas systems with nonlocal short-range interactions additionally exhibit a continuous phase transition to patterned phases. Only the latter system allows for the coexistence of homogeneous and patterned phases, which we explain by mapping to the conserved Swift-Hohenberg model. Taken together, our generic model reveals an underlying framework that describes similar phenomena observed in many complex phase-separating systems.

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Phys. Rev. Research 8, L022023– Published 4 May, 2026
  • Received 6 November 2025
  • Accepted 11 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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