EQUIVALENCE OF THE O(N) VECTOR FERROMAGNETIC AND ANTIFERROMAGNETIC MODELS

The effective-field renormalization group (EFRG) approach is used to f ind the Ni el temperature (T-N) of the O(n) vector model with antiferr omagnetic (AF) interaction. The EFRG method is illustrated by employin g approximations in which clusters with one (N' = 1) and two (N = 2) s pins 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 f erromagnetic (F) case. As a comparison, the results of the quantum Hei senberg model (n = 3) with F and AF interactions are also presented, a nd we find that T-N > T-c, which is different from the classical resul t T-c = T-N. (C) 1998 Published by Elsevier Science B.V. All rights re served.