Improved bounds on cluster expansion of the abstract polymer model (via the Penrose identity)
Seminar Room 1, Newton Institute
The classical approach to cluster expansions, based on tree graphs, is revisited and a new convergence condition that improves those by Kotecky-Preiss and Dobrushin is established, as we show in some examples. The two ingredients of our approach are: (i) a careful consideration of the Penrose identity for truncated functions in the special case of hard core interactions, and (ii) the use of iterated transformations to generate expansions in terms of tree graphs.
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