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Geometric frustration effects in the spin-1 antiferromagnetic Ising model on the kagome-like recursive lattice: exact results

The antiferromagnetic spin-1 Ising model is studied on the Husimi lattice constructed from elementary triangles with coordination number z  =  4. It is found that the model has a unique solution for arbitrary values of the magnetic field as well as for all temperatures. A detailed analysis of the magnetization is performed and it is shown that in addition to the standard plateau-like ground states, the model also contains well-defined single-point ground states related to definite values of the magnetic field. Exact values of the residual entropies for all ground states are found. The properties of the susceptibility and the specific heat of the model are also discussed. The existence of the Schottky-type behavior of the specific heat and the strong magnetocaloric effect for low enough temperatures and for the external magnetic field close to the values at which the single-point ground states exist are identified.