Thermodynamics of O(N) antiferromagnets in 2+1 dimensions

Within the framework of effective Lagrangians we calculate the free energy density for an O(N) antiferromagnet in 2 + 1 dimensions up to three-loop order in the perturbative expansion and derive the low-temperature series for various thermodynamic quantities. In particular, we show that the magnon-magnon interaction in the O(3) antiferromagnet in d=2 + 1-the O(3)-invariant quantum Heisenberg antiferromagnet on a square or a honeycomb lattice-is very weak and repulsive and manifests itself through a term proportional to five powers of the temperature in the free energy density. Remarkably, the corresponding coefficient is fully determined by the leading-order effective Lagrangian L-eff(2) and does not involve any higher-order effective constants from L-eff(4) related to the anisotropies of the lattice-the symmetries are thus very restrictive in d=2 + 1. We also compare our results that apply to O(N) antiferromagnets in 2 + 1 dimensions with those for O(N) antiferromagnets in 3 + 1 dimensions. The present work demonstrates the efficiency of the fully systematic effective Lagrangian method in the condensed-matter domain, which clearly proves to be superior to spin-wave theory. We would like to emphasize that the structure of the low-temperature series derived in the present work is model independent and universal as it only relies on symmetry considerations.