2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18410We consider the influence on the surface critical behaviour of a quantum Ising chain of quenched random surface perturbations decaying as a power of the distance from the surface (random Hilhorst-van Leeuwen models). We study, analytically and numerically, the multiscaling behaviour of the surface magnetization and the surface energy density in the case of marginal perturbations.14 pages, 5 figures, LaTeX2e, epsf, elsartStatistical MechanicsDisordered Systems and Neural Networkstext