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

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.

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

References in corpus (2)

• The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma
• Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model Partition Functions

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