Communications in Mathematical Physics

, Volume 288, Issue 2, pp 731–744 | Cite as

Phase Transition in the 1d Random Field Ising Model with Long Range Interaction

  • Marzio Cassandro
  • Enza Orlandi
  • Pierre PiccoEmail author


We study one–dimensional Ising spin systems with ferromagnetic, long–range interaction decaying as n −2+α , \({\alpha \in\left(\frac 12,\frac{\ln 3}{\ln2}-1\right)}\), in the presence of external random fields. We assume that the random fields are given by a collection of symmetric, independent, identically distributed real random variables, gaussian or subgaussian. We show, for temperature and strength of the randomness (variance) small enough, with IP = 1 with respect to the random fields, that there are at least two distinct extremal Gibbs measures.


Long Range Gibbs Measure Range Interaction Gibbs State Interface Point 
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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversitá di Roma “La Sapienza”RomaItaly
  2. 2.Dipartimento di MatematicaUniversitá di Roma TreRomaItaly
  3. 3.LATP, CMI, UMR 6632, CNRS, Université de ProvenceMarseille Cedex 13France

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