Dimers for Type D Relativistic Toda Model

We construct dimer graphs for type D relativistic Toda models by introducing impurities to the $Y^{2N,0}$ square dimer graphs. By properly placing the impurities and change of canonical variables assigned to the 1-loops on the dimer graph, we introduce the “folding” of the graphs and get the type D relativistic Toda lattice Hamiltonian and monodromy matrix.