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Autre Publication Scientifique Année : 2010

Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction.

Marzio Cassandro
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Enza Orlandi
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Résumé

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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Dates et versions

hal-00540977 , version 1 (29-11-2010)

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Marzio Cassandro, Enza Orlandi, Pierre Picco. Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction.. 2010. ⟨hal-00540977⟩
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