Universality in the critical exponents delta and eta

The critical exponents delta and eta are obtained for the three-dimensional quantum spin-1/2 anisotropic Heisenberg (QAH) model by the mean field reno rmalization group (MFRG) approach. The method is illustrated using its simp lest approximation version in which clusters with N = 1, 2, 4 and 8 spins a re used. the exponents delta and eta are numerically estimated as a functio n of the anisotropy parameter Delta (Delta = 0 and Delta = 1 correspond to the isotropic Heisenberg and ising models, respectively) for all renormaliz ation between clusters of sizes N greater than or equal to 2. In all types of renormalizations the exponents analysed are independent of Delta. I also have studied the classical D-vector model by MFRG approach wit clusters of sizes N' = 1 and N = 2 spins. It was observed that delta and eta do not de pend on D and the numerical results are equivalent to the quantum case with the same clusters in MFRG approach. The results, qualitative and quantitat ive, of the present work are in excellent agreement with more accurate meth ods (Monte Carlo and series expansion). (C) 1999 Elsevier Science B.V.