Study of surface effects in quantum Heisenberg and XY antiferromagnets

Using a finite-cluster mean-field approximation, we study the characteristi cs of phase transitions for the semi-infinite simple cubic quantum spin-1/2 anisotropic Heisenberg model with ferromagnetic and antiferromagnetic inte ractions. The dependence of the critical temperature on the parameter Delta is obtained, where Delta = J(s)/J(b) - 1, J(s) and J(b) are the nearest-ne ighbour coupling constants at the surface and bulk, respectively. Particula r attention has been drawn to the difference between the criticality for th e F (ferromagnetic) and AF (antiferromagnetic) models. It is shown that qua ntum influence modifies the criticality of the anisotropic Heisenberg model with T-c (F case) < T-N (AF case) and T-c > T-N in the bulk-paramagnetic a nd surface paramagnetic critical lines, respectively. On the other hand, th e quantum XY model presents the same criticality for the two types of inter actions (F and AF).