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

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