Reentrance in the phase diagram of the quantum spin 1/2 anisotropic Heisenberg antiferromagnet

The very recently improved treatment proposed by de Sousa and Plascak [Phys . Lett. A 237 (1997) 66], the mean field renormalization group (MFRG) appro ach used on the quantum spin 1/2 Heisenbeg 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 anisotropy parameter (Delta) on a square lattice. Within this approach, we find that T-N is triple valued under cert ain condition of quantum competiting interaction (Delta near of Delta(c) = 0.18), suggesting the occurrence of reentrant behavior in the phase diagram . A preliminary analysis of finite size scaling in small cluster is present ed, showing that the reentrance can be an effect of duster finite size. (C) 2000 Published by Elsevier Science B.V. PACS: 74.72.Dn; 75.30.Kz; 75.50.El .