%0 Unpublished work
%T Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction.
%+ Dipartimento di Fisica
%+ Dipartimento di Matematica [Roma TRE]
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%A Cassandro, Marzio
%A Orlandi, Enza
%A Picco, Pierre
%Z GREFI-MEFI Prin07: 20078XYHYS
%9 Article
%8 2010-11-29
%D 2010
%Z 1011.6487
%K phase transition
%K long--range interaction
%K random field
%Z Primary 60K35, secondary 82B20,82B43
%Z Mathematics [math]/Probability [math.PR]Other publications
%X 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 $\a=1/2$.
%G English
%Z GREFI-MEFI
%2 https://hal.science/hal-00540977/document
%2 https://hal.science/hal-00540977/file/COPF7.pdf
%L hal-00540977
%U https://hal.science/hal-00540977
%~ LATP
%~ CNRS
%~ UNIV-AMU
%~ I2M