Cluster expansion for abstract polymer models. New bounds from an old approach
Mathematical Physics
2009-11-11 v2 math.MP
Abstract
We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients of our approach are: (i) a careful consideration of the Penrose identity for truncated functions, and (ii) the use of iterated transformations to bound tree-graph expansions.
Keywords
Cite
@article{arxiv.math-ph/0605041,
title = {Cluster expansion for abstract polymer models. New bounds from an old approach},
author = {Roberto Fernandez and Aldo Procacci},
journal= {arXiv preprint arXiv:math-ph/0605041},
year = {2009}
}
Comments
16 pages. This new version, written en reponse to the suggestions of the referees, includes more detailed introductory sections, a proof of the generalized Penrose identity and some additional results that follow from our treatment