Revisiting the combinatorics of the 2D Ising model
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.
Cite
@article{arxiv.1507.08242,
title = {Revisiting the combinatorics of the 2D Ising model},
author = {Dmitry Chelkak and David Cimasoni and Adrien Kassel},
journal= {arXiv preprint arXiv:1507.08242},
year = {2019}
}
Comments
Minor change in the notation (definition of eta). 55 pages, 4 figures