Simplex transformations of the spin-1/2 Ising model. I

Abstract

The problems of developing power series expansions for the thermodynamic functions of the spin‐1/2 Ising model are discussed. The basis of the discussion is a generalized Ising‐type model which incorporates collective potentials between special groups of k particles on the lattice sites. The addition of these k‐body potential functions throws a new light onto the problems of developing series expansions for the conventional spin‐1/2 Ising model. A system of transformation equations connecting the high and low temperature series developments of the model is obtained which contains the well‐known high‐low transformation of the Ising model. It is likely that this generalized transformation will provide a useful additional technique in the theory of the conventional Ising model, as well as providing a basis for the discussion of other lattice models which exhibit critical phenomena.