The combinatorial mutation of polygons, which makes a given lattice polygon another one, is an important operation to understand mirror partners for two-dimensional Fano manifolds, and the mutation-equivalent polygons give the $mathbb{Q}$-Gorenstein deformation-equivalent toric varieties. On the other hand, for a dimer model, which is a bipartite graph described on the real two-torus, we assign the lattice polygon called the perfect matching polygon. It is known that for each lattice polygon $P$ there exists a dimer model such that it gives $P$ as the perfect matching polygon and satisfies the consistency condition. Moreover, a dimer model has rich information regarding toric geometry associated with the perfect matching polygon. In this paper, we introduce a set of operations that we call the deformations of consistent dimer models, and show that the deformations of consistent dimer models induce the combinatorial mutations of the associated perfect matching polygons.
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