Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 337 / 2 / a / Solution

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.