Equivalence of the O(n) vector ferromagnetic and antiferromagnetic models

The effective-field renormalization group (EFRG) approach is used to find the Ni el temperature (T-N) of the O(n) vector model with antiferromagnetic (AF) interaction. The EFRG method is illustrated by employing approximations in which clusters with one (N' = 1) and two (N = 2) spins are used. The critical temperature T-N is obtained as a function of component (n) and coordination(z) numbers. For all values of n and z we show that T-N = T-c, where T-c is the Curie temperature for the ferromagnetic (F) case. As a comparison, the results of the quantum Heisenberg model (n = 3) with F and AF interactions are also presented, and we find that T-N > T-c, which is different from the classical result T-c = T-N. (C) 1998 Published by Elsevier Science B.V. All rights reserved.