The Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations

We study the topological defects in the classical Heisenberg antiferromagnet in two dimensions on a triangular lattice (HAFT). While the topological analysis of the order parameter space indicates that the defects are of Z 2 -type, consideration of the energy leads us to a description of the low-energy stationary points of the action in terms of ± vortices, as in the planar XY model. Starting with the continuum description of the HAFT, we show analytically that its partition function can be reduced to that of a 2-dimensional Coulomb gas with logarithmic interaction. Thus, at low temperatures, the correlation length is determined by the spin waves, while at higher temperatures we expect a crossover to a Kosterlitz-Thouless-type behaviour. The results of recent Monte Carlo calculations of the correlation length are consistent with such a crossover.