Abstract
The effect of surface and bulk transverse fields on the phase transitions of a semi-infinite spin-1 ferromagnetic Ising model is investigated within a finite cluster approximation with an expansion technique for cluster identities of spin-1 localized spin systems. The phase diagrams are determined as a function of the ratio of bulk and surface transverse fields, the temperature and the transverse field of the surface. They show that the systems exhibit a variety of phase transitions. A dead layer is also obtained in a special region of space parameters.
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