# 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.
keyword :
Type de document :
Pré-publication, Document de travail
38 pages, 26 figures. 2014
Domaine :

https://hal.archives-ouvertes.fr/hal-00933935
Contributeur : Béatrice De Tilière <>
Soumis le : mardi 21 janvier 2014 - 12:56:53
Dernière modification le : jeudi 11 janvier 2018 - 06:12:29

### Identifiants

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

### Citation

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

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