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The Monopole-Dimer Model for Cartesian Products of Graphs: Extended Abstract

Arora, A and Ayyer, A (2022) The Monopole-Dimer Model for Cartesian Products of Graphs: Extended Abstract. In: Seminaire Lotharingien de Combinatoire (86).

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The monopole-dimer model is a signed variant of the monomer-dimer model which has determinantal structure. We extend the monopole-dimer model for planar graphs introduced by the second author (Math. Phys. Anal. Geom., 2015) to Cartesian products thereof and show that the partition function of this model can be expressed as a determinant of a generalised signed adjacency matrix. We then give an explicit product formula for three-dimensional grid graphs a la Kasteleyn and Temperley–Fischer, in which case the partition function turns out to be fourth power of a polynomial when all grid lengths are even. Finally, we generalise this product formula to k dimensions, again obtaining an explicit product formula.

Item Type: Journal Article
Publication: Seminaire Lotharingien de Combinatoire
Publisher: Universitat Wien, Fakultat fur Mathematik
Additional Information: The copyright for this article belongs to the Universitat Wien, Fakultat fur Mathematik.
Keywords: Cartesian product; dimer model; monopole-dimer model; Pfaffian orientation; plane graph
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 11 Jul 2023 06:28
Last Modified: 11 Jul 2023 06:28
URI: https://eprints.iisc.ac.in/id/eprint/82422

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