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Dimers and cluster integrable systems
2013
Annales Scientifiques de l'Ecole Normale Supérieure
We show that the dimer model on a bipartite graph Γ on a torus gives rise to a quantum integrable system of special type, which we call a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space L Γ of line bundles with connections on the graph Γ. The sum of Hamiltonians is essentially the partition function of the dimer model. 5.3 Cluster nature of the resistor network space .
doi:10.24033/asens.2201
fatcat:td6pyut3jjd5taelz6psl2rlqa