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) $\to$ O(N--1). The leading coefficients of the low temperature expansion for the partition function are calculated up to and including three loops. Emphasis is put into the special case N=3: it describes the antiferromagnet which has been extensively studied. Our results obtained within the framework of the effective Lagrangian technique are compared with the literature. In particular, we show that, at order $T^7$ for the heat capacity and $T^6$ for the order parameter, respectively, logarithmic terms appear in the low temperature expansion, which have been overlooked so far.