Journal | Journal of Statistical Physics |
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Date | E-pub ahead of print - 22 Apr 2014 |
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Date | Published (current) - Jul 2014 |
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Issue number | 1 |
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Volume | 156 |
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Number of pages | 21 |
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Pages (from-to) | 156-176 |
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Early online date | 22/04/14 |
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Original language | English |
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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.