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| HAL : hal-00540977, version 1 |
| arXiv : 1011.6487 |
| Fiche détaillée |  Récupérer au format |
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| Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction. |
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| Marzio Cassandro 1Enza Orlandi 2 |
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| GREFI-MEFI Collaboration(s) |
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| (29/11/2010) |
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| We study a one--dimensional Ising spin systems with ferromagnetic, long--range interaction decaying as $n^{-2+\a}$, $\a \in [0,\frac 12]$, 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 with variance $\theta$. We show that for temperature and variance of the randomness small enough, with an overwhelming probability with respect to the random fields, the typical configurations, within volumes centered at the origin whose size grow faster than any power of $\th^{-1}$, % {\bf around the origin} are intervals of $+$ spins followed by intervals of $-$ spins whose typical length is $ \simeq \th^{-\frac{2}{(1-2\a)}}$ for $0\le \a<1/2$ and $\simeq e^{\frac 1 {\th^{2}}}$ for $\a=1/2$. |
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| 1 : | Dipartimento di Fisica |
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Università degli Studi di Roma |
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| 2 : | Dipartimento di Matematica [Roma TRE] |
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Università degli Studi Roma TRE |
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| 3 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Domaine | : | Mathématiques/Probabilités |
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| phase transition – long--range interaction – random field |
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| hal-00540977, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00540977 | |
| oai:hal.archives-ouvertes.fr:hal-00540977 | |
| Contributeur : Pierre Picco | |
| Soumis le : Lundi 29 Novembre 2010, 15:35:54 | |
| Dernière modification le : Mardi 30 Novembre 2010, 10:02:40 | |
