Squareness for the Monopole-Dimer Model

Ayyer, A (2020) Squareness for the Monopole-Dimer Model. In: Annals of Combinatorics .

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Abstract

The monopole-dimer model introduced recently is an exactly solvable signed generalisation of the dimer model. We show that the partition function of the monopole-dimer model on a graph invariant under a fixed-point free involution is a perfect square. We give a combinatorial interpretation of the square root of the partition function for such graphs in terms of a monopole-dimer model on a new kind of graph with two types of edges which we call a dicot. The partition function of the latter can be written as a determinant, this time of a complex adjacency matrix. This formulation generalises Wu�s assignment of imaginary orientation for the grid graph to planar dicots. As an application, we compute the partition function for a family of non-planar dicots with positive weights.

Item Type:	Journal Article
Publication:	Annals of Combinatorics
Publisher:	Birkhauser
Additional Information:	Copyright of this article belongs to Birkhauser
Keywords:	Monopole-dimer model ; Dicots; Dimer model; Determinantal formula; Kasteleyn orientation; Partition function; Free energy
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	29 Jan 2020 05:23
Last Modified:	29 Jan 2020 05:23
URI:	http://eprints.iisc.ac.in/id/eprint/64406

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