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Cluster expansion for abstract polymer models. New bounds from an old approach. (English) Zbl 1206.82148
Summary: We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecký-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.

MSC:
82D60 Statistical mechanics of polymers
82B05 Classical equilibrium statistical mechanics (general)
05C05 Trees
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