# 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.
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Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00933935
Contributor : Béatrice de Tilière <>
Submitted on : Tuesday, January 21, 2014 - 12:56:53 PM
Last modification on : Friday, March 27, 2020 - 3:05:57 AM

### Identifiers

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

### Citation

B. de Tilière. Critical Ising model and spanning trees partition functions. 2014. ⟨hal-00933935⟩

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