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

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

2010-11-30

arxiv.org/abs/1011.6487v1

Mathematics

Probability

Scientific paper

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 $\a=1/2$.

Affiliated with

Also associated with

No associations

Rating

Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-444904