Critical behavior of the quantum spin- anisotropic Heisenberg model

A two-step renormalization group approach – a decimation followed by an effective field renormalization group (EFRG) – is proposed in this work to study the critical behavior of the quantum spin- anisotropic Heisenberg model. The new method is illustrated by employing approximations in which clusters with one, two and three spins are used. The values of the critical parameter and critical exponent, in two- and three-dimensional lattices, for the Ising and isotropic Heisenberg limits are calculated and compared with other renormalization group approaches and exact (or series) results.