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

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

2008-04-23

arxiv.org/abs/0804.3672v2

Mathematics

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Scientific paper

10.1007/s00220-009-0778-4

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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