Abstract
The effect of the surface and bulk transverse fields on the phase diagrams of a semi-infinite spin-1 ferromagnetic Ising model with a crystal field is investigated within a finite cluster approximation with an expansion technique for cluster identities of spin-1 localized spin systems. Phase diagrams are determined as a function of the ratio of bulk and surface transverse fields and the ratio of bulk and surface crystal fields. However, the system exhibits a variety of phase transitions and multi-critical points. A dead layer appears in a special region of the space parameters.
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