The Green's function of a finite-gap Schr\"odinger operator discretization on a quad graph

We are using the finite-gap approach for the construction of the Schr\"{o}dinger operator discretization on a quad graph. The latter is represented by a two-dimensional integer sublattice in a $d$-dimensional space. The Green's function of the operator can be posed explicitly as an integral of the differential built by the spectral data, calculated on contours of the special form. We also know the the asymptotics of the achieved function.