Generalized transfer formalism and application to random Ising models

We derive an exact formula for the critical temperature of any planar Ising model built up by periodic repetition of an elementary cell. It is shown that the weight of models with analytic free energy increases with increasing size of the elementary cell. As an application we discuss phase diagrams of Ising models with restricted randomness where the coupling arrangement is governed by the probability law of the popular binary distribution.Work performed within the research program of the Sonderforschungsbereich 125 Aachen/Jülich/Köln; also part of: P. Hoever, Dissertation, Köln 1981 (unpublished)