On the convergence of Kikuchi's natural iteration method

In this article we investigate on the convergence of the natural iteration method, a numerical procedure widely employed in the statistical mechanics of lattice systems, to minimize Kikuchi's cluster variational free energies. We discuss a sufficient condition for the convergence, based on the coefficients of the cluster entropy expansion, depending on the lattice geometry. We also show that such a condition is satisfied for many lattices usually studied in applications. Finally, we consider a recently proposed class of methods for the minimization of Kikuchi functionals, showing that the natural iteration method turns out as a particular instance of that class.