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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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