Damping of spin waves in a two-dimensional Heisenberg antiferromagnet at low temperatures

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Abstract
The Dyson-Maleev formalism is used to calculate the damping of spin waves in the two-dimensional Heisenberg antiferromagnet at asymptotically low temperatures and long wavelengths, both in the quantum and in the classical case. The calculations are done self-consistently. Various regimes are found for the decay rate depending on the relative size of the reduced temperature τ and the dimensionless wave vector ka. In all cases, the decay rate is found to be much smaller than the frequency of the excitations, leading to well-defined spin waves, provided that kξ≫1, where the correlation length ξ is of order exp(const/τ). At low but finite temperatures, we take into account fluctuation renormalizations which tend to increase the damping. The result of simulations on the classical lattice rotor model are presented and compared with the calculations. The agreement is qualitatively good. The simulations are also used to test the scaling form for the decay rate in the regime kξ∼1, which is outside the limit of validity of our direct spin-wave calculations.