Quantum influence in the criticality of the spin-1/2 anisotropic Heisenberg model

We study the spin-1/2 anisotropic Heisenberg antiferromagnetic model using the effective held renormalization group (EFRG) approach. The EFRG method is illustrated by employing approximations in which clusters with one (N' = 1) and two (N = 2) spins are used. The dependence of the critical temperature T-c (ferromagnetic-F case) and T-N (antiferromagnetic-AF case) and thermal critical exponent, Y-t, are obtained as a function of anisotropy parameter (Delta) on a simple cubic lattice. We find that, in our results, T-N is higher than T-c for the quantum anisotropic Heisenberg limit and T-N = T-c for the Ising and quantum XY limits. We have also shown that the thermal critical exponent Y-t for the isotropic Heisenberg model shows a small dependence on the type of interaction (F or AF) due to finite size effects. (C) 1999 Elsevier Science B.V. All rights reserved.