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arXiv · 1507.08242

Revisiting the combinatorics of the 2D Ising model

Dmitry Chelkak·David Cimasoni·Adrien Kassel
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Abstract

We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants, using the language of Kac-Ward matrices. We also give a brief account of the relations between various alternative formalisms which have been used in the combinatorial study of the planar Ising model: dimers and Grassmann variables, spin and disorder operators, and, more recently, s-holomorphic observables. In addition, we point out that these formulas can be extended to the double-Ising model, defined as a pointwise product of two Ising spin configurations on the same discrete domain, coupled along the boundary.

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Dmitry Chelkak, David Cimasoni, Adrien Kassel. 2015-07-29. Revisiting the combinatorics of the 2D Ising model. https://doi.org/10.4171/aihpd/42

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