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

Abstract

We consider a one dimensional ferromagnetic Ising spin system with interactions that correspond to a $1/r^2$ 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.

References in corpus (2)

• Geometry of contours and Peierls estimates in d=1 Ising models
• Oriented Percolation in One-Dimensional 1/|x-y|^2 Percolation Models