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

Roberto Fernandez·Aldo Procacci
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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.

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Roberto Fernandez, Aldo Procacci. 2006-10-16. Cluster expansion for abstract polymer models. New bounds from an old approach. https://doi.org/10.1007/s00220-007-0279-2

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