Dimer models and box Sample Clauses

Dimer models and box counting‌ The important equivalence of counting of paths and counting of dimers on graphs was observed in the context of cluster integrable systems in [71],[55]. The statistical models of random dimer configurations are well- studied [105], [118], and are free fermionic, and all correlators and parti- tion function of the model might have been written using the minors of Kasteleyn operator, which is basically just the weighted adjacency matrix of the underlying graph. The spectral curve, which is generating function of Hamiltonians of the cluster integrable system was written in [71] in the form (1.97). It was also shown there, how to construct cluster inte- xxxxxx system with the arbitrary Newton polygon of the spectral curve. The coordinates on phase space of cluster integrable system are -cluster coordinates xf , which can be conveniently interpreted as monodromies of discrete R>0 connection around the faces f of the graph. They are natu- rally constrained by the condition f xf = 1 because of the triviality of