## Abstract

We consider a general class of disordered mean-field models where both the spin variables and disorder variables eta take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate describing the probabilities to find a large system close to a particular convex combination of the pure infinite-volume states. We show that, under a non-degeneracy assumption, only pure states j are seen, with non-random probability weights w (j) for which we derive explicit expressions in terms of interactions and distributions of the disorder variables. We provide a geometric construction distinguishing invisible states (having w (j) =0) from visible ones. As a further consequence we show that, in the case where precisely two pure states are available, these must necessarily occur with the same weight, even if the model has no obvious symmetry relating the two.

Original language | English |
---|---|

Pages (from-to) | 27-55 |

Number of pages | 29 |

Journal | Journal of Statistical Physics |

Volume | 140 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul-2010 |

## Keywords

- Gibbs measures
- Mean-field systems
- Disordered systems
- Metastates
- Ising model
- Potts model
- CURIE-WEISS MODEL
- SPIN-GLASSES
- ISING-MODEL
- BREAKING
- STATES
- LIMIT