A Phase Transition in a Quenched Amorphous Ferromagnet

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JournalJournal of Statistical Physics
DateE-pub ahead of print - 22 Apr 2014
DatePublished (current) - Jul 2014
Issue number1
Volume156
Number of pages21
Pages (from-to)156-176
Early online date22/04/14
Original languageEnglish

Abstract

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.

    Research areas

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

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