Scientific article
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English

The critical temperature for the Ising model on planar doubly periodic graphs

Published inElectronic journal of probability, vol. 18, no. 44, p. 1-18
Publication date2013
Abstract

We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse temperature beta is obtained as the unique solution of an algebraic equation in the variables (tanh(beta J_e)_{ein E(G)}. This is achieved by studying the high-temperature expansion of the model using Kac-Ward matrices.

Classification
  • arxiv : math-ph
Citation (ISO format)
CIMASONI, David, DUMINIL-COPIN, Hugo. The critical temperature for the Ising model on planar doubly periodic graphs. In: Electronic journal of probability, 2013, vol. 18, n° 44, p. 1–18. doi: 10.1214/ejp.v18-2352
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Article (Accepted version)
accessLevelPublic
Identifiers
Journal ISSN1083-6489
622views
515downloads

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Creation20/10/2013 21:48:00
First validation20/10/2013 21:48:00
Update time14/03/2023 20:33:38
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