= Checkerboard decimation of the square-lattice Ising model
{title2=$x+y\equiv0\pmod2\ \text{retained}$}
Checkerboard <spin decimation> retains one parity sublattice of a square-lattice <Ising model> and sums over the other. The retained primitive vectors are $a(1,1)$ and $a(1,-1)$, so the coarse lattice is again square with spacing $\sqrt2a$. A rotation and length rescaling restore the original geometry. Every original nearest-neighbour bond joins the two parity classes, whereas a diagonal next-nearest-neighbour bond stays within one class.
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