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With the convention $H=J{\sum }_{⟨ij⟩}{\sigma }_i{\sigma }_j-h{\sum }_i{\sigma }_i$, positive $J$ favors opposite neighboring Ising spins. On a bipartite graph, the Néel order parameter measures opposite sublattice magnetizations; it is distinct from the uniform magnetization. Changing the signs of spins on one sublattice maps the zero-field model to the ferromagnetic Ising model.

An antiferromagnetic spin wave is a small collective variation of the ordered spin pattern in an antiferromagnet. In a bipartite Néel state, neighbouring spins point oppositely; the slowly varying Néel order parameter describes their staggered orientation. A long-wavelength disturbance changes that orientation smoothly rather than independently flipping each site.

For an isotropic ordered antiferromagnet in the usual long-wavelength regime, the low-energy dispersion relation is linear, $\omega \simeq c|\mathbf{k}|$, with spin-wave velocity $c$. This differs from the quadratic low-wavenumber ferromagnetic magnon in a conventional isotropic ferromagnet. Anisotropy or an applied magnetic field can alter the branches or introduce gaps. The starting ordered state also needs justification: strong quantum fluctuations, especially in low dimension, can invalidate a naive linear spin-wave approximation. A computed divergence is then a warning about the approximation, not a negative physical magnetization.

Let ${\eta }_i=+1$ and $-1$ on the two sublattices of the square lattice. A unit-vector decomposition that separates staggered and uniform magnetization iswhereThe alternating part is the Néel order parameter, while $\mathbf{m}$ is the slowly varying uniform magnetization generated by canting the two sublattices.