Third-order spin-wave theory for the Heisenberg antiferromagnet

Spin-wave perturbation theory for the anisotropic Heisenberg antiferromagnet at zero temperature is carried to third order, using both the Dyson-Maleev and Holstein-Primakoff formalisms. Physical quantities calculated include the ground-state energy, staggered magnetization, staggered parallel susceptibility, transverse susceptibility, and energy gap. For the Holstein-Primakoff formalism, some terms diverge in the isotropic limit, but these divergences eventually cancel one another, and the final results are the same as for the Dyson-Maleev formalism. Applying these results to the square-lattice case, we find that the convergence of the spin-wave theory towards our recent estimates is further improved if we promote the spin-wave theory to third order.