Research output: Contribution to journal › Article

Journal | Journal of Statistical Physics |
---|---|

Date | E-pub ahead of print - 22 Apr 2014 |

Date | Published (current) - Jul 2014 |

Issue number | 1 |

Volume | 156 |

Number of pages | 21 |

Pages (from-to) | 156-176 |

Early online date | 22/04/14 |

Original language | English |

Quenched thermodynamic states of an amorphous ferromagnet are studied. The magnet is a countable collection of point particles chaotically distributed over Rd , d≥2 . Each particle bears a real-valued spin with symmetric a priori distribution; the spin-spin interaction is pair-wise and attractive. Two spins are supposed to interact if they are neighbors in the graph defined by a homogeneous Poisson point process. For this model, we prove that with probability one: (a) quenched thermodynamic states exist; (b) they are multiple if the intensity of the underlying point process and the inverse temperature are big enough; (c) there exist multiple quenched thermodynamic states which depend on the realizations of the underlying point process in a measurable way.

- Random Gibbs measure, Geometric random graph, Poisson point process, Percolation, Unbounded spin model, Wells inequality

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