English

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}
}
R2 v1 2026-06-21T10:33:48.730Z