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Critical properties of Ising multilayer systems: cluster approximation

The theoretical framework for investigating the critical behaviour of an Ising multilayer system consisting of alternating spin-1/2 and spin-S (S½) magnetic layers is given within the cluster approximation introduced into the differential operator technique. It has the statistical accuracy corresponding to the Bethe-Peierls approximation. The critical temperatures TC of some multilayer systems are studied numerically. We find some characteristic features, including the behaviour of a critical transverse field in the transverse spin-1/2 ferromagnetic multilayer system and the different behaviour of the TC curve in an alternating spin-1/2 and spin-S (S>½) Ising multilayer system, depending on whether S is an integer or a half-integer.