Local critical behaviour at aperiodic surface extended perturbation in the Ising quantum chain

摘要

The surface critical behaviour of the semi--infinite one--dimensional quantumIsing model in a transverse field is studied in the presence of an aperiodicsurface extended modulation. The perturbed couplings are distributed accordingto a generalized Fredholm sequence, leading to a marginal perturbation andvarying surface exponents. The surface magnetic exponents are calculatedexactly whereas the expression of the surface energy density exponent isconjectured from a finite--size scaling study. The system displays surfaceorder at the bulk critical point, above a critical value of the modulationamplitude. It may be considered as a discrete realization of the Hilhorst--vanLeeuwen model.