Identifying interacting pairs of sites in infinite range Ising models

We consider Ising models (pairwise interaction Gibbs probability measures) in $\Z^d$ with an infinite range potential. We address the problem of identifying pairs of interacting sites from a finite sample of independent realisations of the Ising model. The sample contains only the values assigned by the Ising model to a finite set of sites in $\Z^d$. Our main result is an upperbound for the probability with our estimator to misidentify the pairs of interacting sites in this finite set.