Effective analysis of the O(N) antiferromagnet: Low-temperature expansion of the order parameter

We investigate the low-energy properties of Lorentz-invariant theories with a spontaneously broken rotation symmetry O(N)-->O(N- I). The leading coeff icients of the low-temperature expansion for the partition function are cal culated up to and including three loops. Emphasis is put into the special c ase N=3: it describes the antiferromagnet which has been extensively studie d. Our results obtained within the framework of the effective Lagrangian te chnique are compared with the literature. In particular, we show that, at o rder T-eta for the heat capacity and T-6 for the order parameter, respectiv ely, logarithmic terms appear in the low-temperature expansion, which have been overlooked so far. [S0163-1829(99)02325-5].