We consider a three-dimensional Ising model in a transverse magnetic f
ield h and a bulk field H. An interface is introduced by an appropriat
e choice of boundary conditions. At the point (H=0, h=0) spin configur
ations corresponding to different positions of the interface are degen
erate. By studying the phase diagram near this multiphase point using
quantum mechanical perturbation theory, we show that the quantum fluct
uations, controlled by h, split the multiphase degeneracy giving rise
to an infinite sequence of layering transitions.