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) approach used on the quantum spin 1/2 Heisenberg antiferromagnet in two sublattices, is herein extended for larger clusters (two and four spins). The critical temperature for the ferromagnetic, Tc(F) and antiferromagnetic, TN (AF) are obtained as a function of the interlayer parameter (λ). Within this approach, we find that TN is double valued under certain condition of λ (λ near of λc=0.50), suggesting the occurrence of reentrant 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.