Multiscaling in Ising quantum chains with random Hilhorst–van Leeuwen perturbations

We 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.