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 techn
ique for duster identities of spin-1 localized spin systems. Phase diagrams
are determined as a function of the ratio of bulk and surface transverse f
ields 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. (C) 1999 Elsevie
r Science B.V. All rights reserved.