Cluster expansion for abstract polymer models. New bounds from an old approach

Details Cluster expansion for abstract polymer models. New bounds from an old approach Cluster expansion for abstract polymer models. New bounds from an old approach

2006-05-12

arxiv.org/abs/math-ph/0605041v2

Physics

Mathematical Physics

16 pages. This new version, written en reponse to the suggestions of the referees, includes more detailed introductory section

Scientific paper

10.1007/s00220-007-0279-2

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.

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