= Hypercubic antiferromagnetic spin-wave dispersion
{title2=$\omega_{\mathbf k}=2dJS\sqrt{1-\gamma_{\mathbf k}^2}$}
For a nearest-neighbour <Heisenberg antiferromagnet> on a <hypercubic lattice>, the <linear spin-wave approximation> gives $\gamma_{\mathbf k}=d^{-1}\sum_j\cos(k_ja)$ and the displayed frequency. Near a gapless point its <spin-wave velocity> is $2JSa\sqrt d$. Its ground-state boson occupation is $[1/\sqrt{1-\gamma_{\mathbf k}^2}-1]/2$, producing <quantum depletion of Néel order>. Exact zero modes need an infrared regulator or separate global-rotation treatment.
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