= Heisenberg-chain spin-wave comparison
{c}
{title2=$\omega_F(k)=2JS(1-\cos k),\quad\omega_{AF}(k)=2JS|\sin k|$}
With unit lattice spacing and $\hbar=1$, a nearest-neighbour <Heisenberg model> has quadratic low-momentum <ferromagnetic magnons> and linear antiferromagnetic modes in the <linear spin-wave approximation>. The ferromagnetic polarized vacuum is an exact <ground state>, whereas the assumed antiferromagnetic ordered vacuum has <quantum depletion of Néel order>. In one dimension its logarithmic <infrared divergence> invalidates finite ordered <magnetization> and prevents the linear approximation from deciding the exact gap.
Back to article page
