%0 Journal Article
%T Phase Transition in the 1d Random Field ising model with long range interaction
%A Marzio Cassandro
%A Enza Orlandi
%A Pierre Picco
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/s00220-009-0778-4
%X 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.
%U http://arxiv.org/abs/0804.3672v2