# Critical Ising model and spanning trees partition functions

Authors
Publication Date
Source
Hal-Diderot
Keywords
• Critical Ising Model
• Critical Spanning Trees
• Dimension 2
• Dimers
• 82B20, 82B27, 05A19
• [Phys.Mphy] Physics [Physics]/Mathematical Physics [Math-Ph]
• [Math.Math-Mp] Mathematics [Math]/Mathematical Physics [Math-Ph]
• [Math.Math-Pr] Mathematics [Math]/Probability [Math.Pr]
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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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