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arXiv · 0804.3672

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

Marzio Cassandro·Enza Orlandi·Pierre Picco
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Abstract

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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Marzio Cassandro, Enza Orlandi, Pierre Picco. 2008-12-22. Phase Transition in the 1d Random Field ising model with long range interaction. https://doi.org/10.1007/s00220-009-0778-4

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