Critical Ising model and spanning trees partition functions

Abstract : We prove that the squared partition function of the two-dimensional critical Ising model defined on a finite, isoradial graph $G=(V,E)$, is equal to $2^{|V|}$ times the partition function of spanning trees of the graph $\bar{G}$, where $\bar{G}$ is the graph $G$ extended along the boundary; edges of $G$ are assigned Kenyon's [Ken02] critical weights, and boundary edges of $\bar{G}$ have specific weights. The proof is an explicit construction, providing a new relation on the level of configurations between two classical, critical models of statistical mechanics.
Type de document :
Pré-publication, Document de travail
38 pages, 26 figures. 2014
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https://hal.archives-ouvertes.fr/hal-00933935
Contributeur : Béatrice De Tilière <>
Soumis le : mardi 21 janvier 2014 - 12:56:53
Dernière modification le : mardi 30 mai 2017 - 01:07:52

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  • HAL Id : hal-00933935, version 1
  • ARXIV : 1312.7026

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B. De Tilière. Critical Ising model and spanning trees partition functions. 38 pages, 26 figures. 2014. <hal-00933935>

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