Study of a long range perturbation of a one-dimensional Kac model

We consider a one dimensional ferromagnetic Ising spin system with interactions that correspond to a $1\mathrm{/}{r}^2$ long range perturbation of the usual Kac model. We apply a coarse graining procedure, widely used for higher-dimensional finite range Kac potentials, to describe the basic properties of the system and the relation with the mean field theory.