On the convergence of Kikuchi's natural iteration method

Details On the convergence of Kikuchi's natural iteration method On the convergence of Kikuchi's natural iteration method

2004-04-27

arxiv.org/abs/cond-mat/0404654v1

Physics

Condensed Matter

Statistical Mechanics

18 pages, 1 table, 1 figure

Scientific paper

10.1007/s10955-005-4426-x

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 general method for the minimization of non convex functionals, showing that the natural iteration method turns out as a particular case of that method.

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