Boundary critical phenomena of the random transverse Ising model in D>=2 dimensions

Using the strong disorder renormalization group method we study numerically the critical behavior of the random transverse Ising model at a free surface, at a corner and at an edge in D=2, 3 and 4-dimensional lattices. The surface magnetization exponents are found to be: x_s=1.60(2), 2.65(15) and 3.7(1) in D=2, 3 and 4, respectively, which do not depend on the form of disorder. We have also studied critical magnetization profiles in slab, pyramid and wedge geometries with fixed-free boundary conditions and analyzed their scaling behavior.