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

Marzio Cassandro (1) , Enza Orlandi (2) , Pierre Picco (3)

1 Dipartimento di Fisica
2 Dipartimento di Matematica [Roma TRE]
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Mots clés: Phase transition; long range interaction

Domaines: Probabilités [math.PR]

Marzio Cassandro, Enza Orlandi, Pierre Picco. Phase Transition in the 1d Random Field ising model with long range interaction. 2008. ⟨hal-00275312v2⟩