= Competing exchanges on a body-centred cubic antiferromagnet
{title2=$J_2/J_1=2/3$}
With $H=\sum_{ij\ \mathrm{bonds}}J_{ij}\mathbf S_i\cdot\mathbf S_j$ counting bonds once, type-I and type-II classical collinear energies per <spin> are $S^2(-4J_1+3J_2)$ and $-3J_2S^2$. Their boundary is $J_2/J_1=2/3$. The corresponding ordering reflections have integer indices with odd sum, and three half-integer indices, respectively, in units of $2\pi/a$. This compares classical order, not an exact quantum product-state <ground state>.
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