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Dimers and Circle patterns. (arXiv:1810.05616v1 [math-ph])
来源于:arXiv
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 circle patterns). As a
consequence the Miquel dynamics on circle patterns is governed by the
octahedron recurrence. As special cases of these circle pattern embeddings, we
recover harmonic embeddings for resistor networks and s-embeddings for the
Ising model. 查看全文>>