Natural iteration method and boundary free energy

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Abstract
The natural iteration technique, which was proposed by the author as a method of solving equations of the cluster variation method, is extended to the case in which variables are subject to subsidiary conditions due to symmetry requirements; the subsidiary conditions are treated by minor iterations at each step of the major iteration. The technique of evaluating the second order transition point for such problems is presented; the technique applies, in general, to problems for which the number of variables is large. As examples, cluster variation methods using a five‐point W‐shaped cluster and a six‐point double‐square cluster are presented for the two dimensional Ising model. An improved proof of the scalar product (SP) expression for the boundary free energy is given. The results of the examples are used in the SP expression to evaluate the boundary free energy of the Ising model in order to test the accuracy of the approximations involved.