Summation of closed diagrams on a square lattice

By the introduction of “rotation” matrices in a four-dimensional space of anticommuting variables, a new representation is constructed for the asymptotic behavior of the generating function of closed diagrams on a square lattice in the thermodynamic limit. The calculations are made by means of integration with respect to anticommuting variables. Selection rules are obtained for the construction of “rotation” matrices with which the solved problem acquires a geometrical meaning.