Scalar φ4 field theory for active-particle phase separation

Raphael Wittkowski*, Adriano Tiribocchi, Joakim Stenhammar, Rosalind J. Allen, Davide Marenduzzo, Michael E. Cates

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Recent theories predict phase separation among orientationally disordered active particles whose propulsion speed decreases rapidly enough with density. Coarse-grained models of this process show time-reversal symmetry (detailed balance) to be restored for uniform states, but broken by gradient terms; hence, detailed-balance violation is strongly coupled to interfacial phenomena. To explore the subtle generic physics resulting from such coupling, we here introduce ‘Active Model B’. This is a scalar φ4 field theory (or phase-field model) that minimally violates detailed balance via a leading-order square-gradient term. We find that this additional term has modest effects on coarsening dynamics, but alters the static phase diagram by creating a jump in (thermodynamic) pressure across flat interfaces. Both results are surprising, since interfacial phenomena are always strongly implicated in coarsening dynamics but are, in detailed-balance systems, irrelevant for phase equilibria.

Original languageEnglish
Article number4351
Number of pages9
JournalNature Communications
Publication statusPublished - 10 Jul 2014




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