Abstract
Using a finite-cluster mean-field approximation, we study the characteristics of phase transitions for the semi-infinite simple cubic quantum spin-1/2 anisotropic Heisenberg model with ferromagnetic and antiferromagnetic interactions. The dependence of the critical temperature on the parameter is obtained, where Δ = J s /J b - 1, J s and J b are the nearest-neighbour coupling constants at the surface and bulk, respectively. Particular attention has been drawn to the difference between the criticality for the F (ferromagnetic) and AF (antiferromagnetic) models. It is shown that quantum influence modifies the criticality of the anisotropic Heisenberg model with T c (F case) T N in the bulk-paramagnetic and surface paramagnetic critical lines, respectively. On the other hand, the quantum XY model presents the same criticality for the two types of interactions (F and AF).
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