## Abstract

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 N_{α}/N=r_{α} 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 ρ_{α}(x) except for some special values of the r_{α} for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature.

Original language | English (US) |
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Pages (from-to) | 763-784 |

Number of pages | 22 |

Journal | Journal of Statistical Physics |

Volume | 145 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2011 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

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