High-temperature expansions for classical spin models

It is shown that the transitivity of the symmetry group of a classical spin model leads to a high-temperature expansion of the free energy of such a model in terms of multiply connected graphs. For models with a completely permissible symmetry group (e.g., for Ising and Potts models), these graphs fall into equivalence classes. Such classes are classified according to their cyclomatic index. Several different methods for obtaining the high-temperature series in a practical way are also discussed. The extension of these results to models with an infinite symmetry group is indicated.