= Classical ground states of an XXZ spin chain
{title2=$E_{\min}=-JNS^2\max(1,|\Delta|)$}
For an even periodic classical chain with <spin> length $S$ and $J>0$, each bond attains the negative largest <singular value> of $\operatorname{diag}(1,1,\Delta)$. For $\Delta>1$ the two minimizing configurations are alternating $z$ <spins>. For $|\Delta|<1$ they are planar <Néel states> with arbitrary in-plane angle. For $\Delta<-1$ the two configurations have uniform $z$ <spins>. At $\Delta=1$ the Néel direction is arbitrary on a sphere; at $\Delta=-1$ a staggered transverse component and uniform longitudinal component parameterize another spherical degeneracy. These are classical configuration manifolds, not a claim about finite quantum-chain degeneracy.
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