Phase Transition in the 1d Random Field Ising Model with Long Range Interaction |
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Authors: | Marzio Cassandro Enza Orlandi Pierre Picco |
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Affiliation: | (1) Dipartimento di Fisica, Universitá di Roma “La Sapienza”, P.le A. Moro, 00185 Roma, Italy;(2) Dipartimento di Matematica, Universitá di Roma Tre, L.go S.Murialdo 1, 00146 Roma, Italy;(3) LATP, CMI, UMR 6632, CNRS, Université de Provence, 39 rue Frederic Joliot Curie, 13453 Marseille Cedex 13, France |
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Abstract: | We study one–dimensional Ising spin systems with ferromagnetic, long–range interaction decaying as n −2+α , , 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. Supported by: GDRE 224 GREFI-MEFI, CNRS-INdAM. P.P was also partially supported by INdAM program Professori Visitatori 2007; M.C and E.O were partially supported by Prin07: 20078XYHYS. |
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