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hal-00275312, version 1

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

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

(2008-04-22)

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.

  • 1:  Dipartimento di Fisica
  • Università degli Studi di Roma
  • 2:  Dipartimento di Matematica [Roma TRE]
  • Università degli Studi Roma TRE
  • 3:  Laboratoire d'Analyse, Topologie, Probabilités (LATP)
  • CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III
  • Collaboration : GDRE 224, GREFI-MEFI CNRS-INdAM
 
  • hal-00275312, version 1
  • http://hal.archives-ouvertes.fr/hal-00275312
  • oai:hal.archives-ouvertes.fr:hal-00275312
  • From: Pierre Picco <>
  • Submitted on: Wednesday, 23 April 2008 11:47:52
  • Updated on: Wednesday, 23 April 2008 11:49:37