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.