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Partition function of periodic isoradial dimer models


de Tilière, B (2007). Partition function of periodic isoradial dimer models. Probability Theory and Related Fields, 138(3-4):451-462.

Abstract

Isoradial dimer models were introduced in Kenyon (Invent Math 150(2):409–439, 2002)—they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of (Kenyon in Invent Math 150(2):409–439, 2002), namely that for periodic isoradial dimer models, the growth rate of the toroidal partition function has a simple explicit formula involving the local geometry of the graph only. This is a surprising feature of periodic isoradial dimer models, which does not hold in the general periodic dimer case (Kenyon et al. in Ann Math, 2006).

Abstract

Isoradial dimer models were introduced in Kenyon (Invent Math 150(2):409–439, 2002)—they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of (Kenyon in Invent Math 150(2):409–439, 2002), namely that for periodic isoradial dimer models, the growth rate of the toroidal partition function has a simple explicit formula involving the local geometry of the graph only. This is a surprising feature of periodic isoradial dimer models, which does not hold in the general periodic dimer case (Kenyon et al. in Ann Math, 2006).

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Language:English
Date:2007
Deposited On:04 Jan 2010 13:19
Last Modified:23 Jan 2022 14:31
Publisher:Springer
ISSN:0178-8051
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00440-006-0041-2
Related URLs:http://arxiv.org/abs/math/0605583
  • Content: Accepted Version
  • Content: Published Version
  • Language: English
  • Description: Nationallizenz 142-005