The Heisenberg antiferromagnet on a triangular lattice: topological excitations

Abstract

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 $\pm$ 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 spinwaves, 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.

9 pages, revtex, preprint: ITP-UH 03/94

References in corpus (1)

• The s=1/2 Heisenberg Antiferromagnet on the Triangular Lattice: Exact Results and Spin-Wave Theory for Finite Cells

Cited by in corpus (15)

• Nonperturbative renormalization group approach to frustrated magnets
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Spin-glass phase of cuprates
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations
• Interplay of anisotropy and frustration: triple transitions in a triangular-lattice antiferromagnet
• Spin-stiffness and topological defects in two-dimensional frustrated spin systems
• The critical behavior of 2-d frustrated spin models with noncollinear order
• Dynamics of topological defects in a spiral: a scenario for the spin-glass phase of cuprates
• Topological Defects and the Spin Glass Phase of Cuprates
• First order transition induced by topological defects in the O(3) principal chiral model
• Interplay of topology and geometry in frustrated 2d Heisenberg magnets
• Berezinskii-Kosterlitz-Thouless transitions in an easy-plane ferromagnetic superfluid
• Hubbard bands, Mott transition and deconfinement in strongly correlated systems
• Dissipative dynamics of topological defects in frustrated Heisenberg spin systems