Complete wetting in the three-dimensional transverse Ising model

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