CRITICAL PROPERTIES OF THE CLASSICAL XY AND CLASSICAL HEISENBERG MODELS - A RENORMALIZATION-GROUP STUDY

By using two approaches of renormalization group (RG), mean field RG ( MFRG) and effective field RG (EFRG, we study the critical properties o f the simple cubic lattice classical XY and classical Heisenberg model s. The methods are illustrated by employing its simplest approximation version in which small clusters with one (N'=1) and two (N=2) spins a re used. The thermal and magnetic critical exponents, Y-t and Y-h, and the critical parameter K-c are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and epsilon- expansion). The results presented in this work are in excellent agreem ent with these sophisticated methods. We have also shown that the expo nent Y-h does not depend on the symmetry n of the Hamiltonian, hence t he criteria of universality for this exponent is only a function of th e dimension d.