The semi-infinite quantum spin-1/2 XY model

The phase transition of the semi-infinite simple cubic quantum spin 1/2 anisotropic XY model is studied by the mean field renormalization group approach. The critical temperature as a function of the Delta parameter is obtained, where Delta = J(s)/J(b-1), J(s) and J(b) are the nearest-neighbor coupling constants at the surface and bulk, respectively. We have also obtained the multicritical point (Delta (c)) and crossover exponent (phi) for the Ising and isotropic XY limits with F and AF interactions.