Percolation Theory and the Ising Model for a Class of Triangular Cactii

A simply applied approximation that was introduced previously by the author [J. Phys. C.: Solid State Phys. 6 (1973), 2089] for calculating Curie temperatures on an arbitrary lattice in the undiluted Ising model of ferromagnetism is considered. It is applied to a complete class of simple triangular branching media for which the necessary lattice constants are obtained exactly. The approximation is again found to be remarkably successful and several of its general characteristics are illustrated in detail. The status of "exact" branching media solutions to this and other problems is discussed critically.