CRITICAL-BEHAVIOR OF THE ANISOTROPIC HEISENBERG-MODEL BY EFFECTIVE-FIELD RENORMALIZATION-GROUP

A real-space effective-field renormalization-group method (ERFG) recen tly derived for computing critical properties of Ising spins is extend ed to treat the quantum spin-1/2 anisotropic Heisenberg model. The for malism is based on a generalized but approximate Callen-Suzuki spin re lation and utilizes a convenient differential operator expansion techn ique. The method is illustrated in several lattice structures by emplo ying its simplest approximation version in which clusters with one (N' = 1) and two (N = 2) spins are used. The results are compared with th ose obtained from the standard mean-field (MFRG) and Migdal-Kadanoff ( MKRG) renormalization-group treatments and it is shown that this techn ique leads to rather accurate results. It is shown that, in contrast w ith the MFRG and MKRG predictions, the EFRG, besides correctly disting uishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in t he isotropic Heisenberg limit. For the simple cubic lattice, the depen dence of the transition temperature T(c) with the exchange anisotropy parameter DELTA[i.e., T(c)(DELTA)], and the resulting value for the cr itical thermal crossover exponent phi [i.e., T(c) congruent-to T(c)(0) +ADELTA1/phi] are in quite good agreement with-results available in th e literature in which more sophisticated treatments are used.