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

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Roberto Fernandez, Aldo Procacci

Mathematical Physics · Submitted 12 May 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv IDmath-ph/0605041 (version 2)
Pith ID2LMD7TO7, Pith's permanent record of this paper and its review
CitationAldo Procacci, Roberto Fernandez. "Cluster expansion for abstract polymer models. New bounds from an old approach." arXiv:math-ph/0605041 (2006). https://pith.science/paper/2LMD7TO7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,335 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 0.91 0.94 0.86 asserted 1.00
s1 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. method 0.97 0.88 0.07 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from proof or derivation 1.00.

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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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References
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4 arXiv papers cite this in 14 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 9 sentences without a confident label

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