Phase diagram on the anisotropic quantum and classical Heisenberg models

The very recently improved treatment proposed by de Sousa and Plascak [Phys . Lett. A237 (1997) 66], the mean field renormalization group (MFRG) approa ch used on the quantum spin 1/2 Heisenberg antiferromagnet in two sublattic es, is herein extended for larger clusters (two and four spins). The critic al temperature for the ferromagnetic, T-c(F) and antiferromagnetic, T-N (AF ) are obtained as a function of the interlayer parameter (lambda). Within t his approach, we find that TN is double valued under certain condition of l ambda (lambda near of lambda(c) = 0.50), suggesting the occurrence of reent rant behavior in the phase diagram. We have also investigated the classical Heisenberg model and compared with results of Monte Carlo simulation. For the quantum Heisenberg model we compare with spin wave theory. (C) 2000 Els evier Science Ltd. All rights reserved.