Phase transition in the ABC model

M Clincy*, B Derrida, MR Evans

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter q describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work, we consider the weak asymmetry regime q=exp(-beta/N), where N is the system size, and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second-order phase transition at some nonzero beta(c). The value of beta(c)=2piroot3 and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean-field equations and analyze some of their predictions.

Original languageEnglish
Article number066115
Number of pages8
JournalPhysical Review E - Statistical, Nonlinear and Soft Matter Physics
Volume67
Issue number6
DOIs
Publication statusPublished - Jun 2003

Keywords

  • DRIVEN DIFFUSIVE SYSTEMS
  • ASYMMETRIC EXCLUSION MODEL
  • LOW AUTOCORRELATION
  • BINARY SEQUENCES
  • FIELD-THEORY
  • LATTICE-GAS
  • SEPARATION
  • STATES
  • CONDENSATION
  • BREAKING

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