2022
DOI: 10.24033/asens.2507
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Dimers and circle patterns

Abstract: We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar or embedded on the torus. The set of positive face weights on the graph gives a set of global coordinates on the space of circle patterns with embedded dual. Under this correspondence, which extends the previously known isoradial case, the urban renewal (local move for dimer models) is equivalent to the Miquel move (local move for ci… Show more

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Cited by 6 publications
(27 citation statements)
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“…A more geometric viewpoint on “nice” gauge functions, the so‐called Coulomb gauges , was suggested in [33]. These gauges have many remarkable algebraic properties (see also [1]) and are also closely related to T‐graphs mentioned above.…”
Section: Introductionmentioning
confidence: 99%
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“…A more geometric viewpoint on “nice” gauge functions, the so‐called Coulomb gauges , was suggested in [33]. These gauges have many remarkable algebraic properties (see also [1]) and are also closely related to T‐graphs mentioned above.…”
Section: Introductionmentioning
confidence: 99%
“…In parallel, a notion of s‐embeddings of graphs carrying the planar Ising model was suggested in [9]. As explained in [33, section 7], the latter are a particular case of the former under the combinatorial bosonization correspondence of the two models [19]. The notion of t‐embeddings discussed in our paper is fully equivalent to Coulomb gauges of [33] except that we focus on embeddings of the dual graphs (scriptGδ)$(\mathcal {G}^\delta )^*$ from the very beginning.…”
Section: Introductionmentioning
confidence: 99%
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