Phase Diagram of a Generalized ABC Model on the Interval

J. Barton, J. L. Lebowitz, E. R. Speer

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4 Scopus citations


We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,...,N is occupied by a particle of type α=A,B,C, with the average density of each particle species Nα/N=rα fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρα(x) except for some special values of the rα for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature.

Original languageEnglish (US)
Pages (from-to)763-784
Number of pages22
JournalJournal of Statistical Physics
Issue number3
StatePublished - Nov 2011

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • External fields
  • Generalized ABC model
  • Phase diagram
  • Scaling limit


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