A theoretical investigation of the effects of surface dilution on spin
waves in a semi-infinite transverse Ising model (TIM) is presented. W
ithin the framework of the double-time Green's function theory, the lo
cal density of spin-wave states is obtained by the application of the
cluster-Bethe-lattice (CBL) method. Numerical calculations of paramagn
etic phases reveal that surface dilution will lead to appearance of th
e localized spin-wave states whose frequencies are bulk independent wh
ile the corresponding density of states is a function of the exchange
interactions. Increase of the bulk exchange interactions between the s
urface and the bulk spins tends to diminish the localized spin-wave st
ates. Dependence of the local density of states on the concentration p
of the magnetic atoms is similar with that in a three-dimensional inf
inite TIM which has been discussed in our previous paper.