Phase Transition in the 1d Random Field ising model with long range interaction
Probability
2009-11-13 v2
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.
Keywords
Cite
@article{arxiv.0804.3672,
title = {Phase Transition in the 1d Random Field ising model with long range interaction},
author = {Marzio Cassandro and Enza Orlandi and Pierre Picco},
journal= {arXiv preprint arXiv:0804.3672},
year = {2009}
}