Phase Transition in the 1d Random Field ising model with long range interaction - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2008

Phase Transition in the 1d Random Field ising model with long range interaction

Marzio Cassandro
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Enza Orlandi
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Résumé

We study the one dimensional Ising model with ferromagnetic, long range interaction which decays as |i-j|^{-2+a}, 1/2< a<1, in the presence of an external random filed. we assume that the random field is given by a collection of independent identically distributed random variables, subgaussian with mean zero. We show that for temperature and strength of the randomness (variance) small enough with P=1 with respect to the distribution of the random fields there are at least two distinct extremal Gibbs measures.
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Dates et versions

hal-00275312 , version 1 (23-04-2008)
hal-00275312 , version 2 (22-12-2008)

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Marzio Cassandro, Enza Orlandi, Pierre Picco. Phase Transition in the 1d Random Field ising model with long range interaction. 2008. ⟨hal-00275312v2⟩
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