Order by disorder in an anisotropic pyrochlore lattice antiferromagnet

The properties of the classical Heisenberg pyrochlore lattice antiferromagnet with local planar single ion anisotropy are discussed. The zero temperature ground state is found to be macroscopically degenerate and without long range order. Monte Carlo simulations are used to investigate the properties of the system at finite temperature. We find that thermal fluctuations select a subset of the ground state manifold, and induce a first-order phase transition to a conventional Néel ground state.