Order by disorder in the classical Heisenberg kagomé antiferromagnet

Antiferromagnetic ordering on a kagome$iaa— net is frustrated by the geometry of the lattice. The infinite number of classical ground states suggests that the system might not order at zero temperature, even for Heisenberg spins. However, high-temperature series expansions and earlier simulations indicate that this degeneracy is resolved by thermal fluctuations (i.e., order by disorder), suggesting a nine-sublattice coplanar Néel-like ordering of the spins. Coplanar nematic, random three-state Potts, and Néel orderings for the Heisenberg kagome$aa— lattice antiferromagnet are investigated with Monte Carlo simulations coupled with state-of-the-art histogram methods for data analysis. We see strong evidence for thermal selection of long-range order with the spin correlations exhibiting algebraic decay, but the low-temperature phases are also seen to posses a chiral domain structure and very short-range chiral correlations. It is argued that the spin correlations are, surprisingly, rather insensitive to this lack of chiral order. Our results are consistent with T=0 being a critical point for this model system.