Summation of topologically equivalent diagrams in the ising model

Convenient rules are formulated for summing lattice diagrams for the calculation of the coefficients of the high-temperature series of the thermodynamic functions of the Ising model. By the standard procedure the lattice diagrams are split into classes of topological equivalence. Diagrams within each class are summed and the problem of finding the free energy and the initial susceptibility is reduced to summing over topological diagrams. An algorithm is constructed for calculating the weight functions and the weight coefficients of the diagrams. It is shown that a phase transition cannot be correctly described by partial summation of the diagrams of the complete series in accordance with any topological criterion.