Solvable Decorated Ising Model with Superexchange Interaction

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Abstract
A rigorously solvable model which combines the Fisher model for a two-dimensional super-exchange antiferromagnet and the Shozi-Miyazima model of a dilute-Ising spin system is proposed. The partition function of the model system can be calculated exactly by making use of Onsager's rigorous solution of the two-dimensional Ising model. In the present model, there are two kinds of ions in each sublattice: One is a magnetic ion and the other is a nonmagnetic ion which does not feel the magnetic field but interacts with the magnetic ions by the exchange force. Further, the effect of the dilution or of the anisotropy—it depends on the interpretation of the parameter in the model Hamiltonian—is taken into account, so that thermodynamic and magnetic quantities of this system are computed as a function of temperature and magnetic field for the fixed values of the magnetic-ion concentration or the anisotropy energy constant. The analysis of the results reveals that there occurs a peculiar phase transition in some range of the parameters. The critical behavior of the thermodynamic quantities is also investigated.

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