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arXiv · 1312.7026

Critical Ising model and spanning trees partition functions

B. de Tilière
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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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B. de Tilière. 2013-12-25. Critical Ising model and spanning trees partition functions. https://arxiv.org/abs/1312.7026

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