= Leading checkerboard Ising decimation recursion
{title2=$K'=L+2K^2,\quad L'=K^2$}
For dimensionless nearest-neighbour coupling $K$ and diagonal coupling $L$, the second cumulant in <checkerboard decimation of the square-lattice Ising model> generates $K^2$ for each pair of retained neighbours of an eliminated centre. A retained diagonal pair shares two centres, and an axial pair at distance $2a$ shares one. The displayed two-coupling recursion neglects $K^4$, $K^2L$, and $L^2$, treating $L$ as order $K^2$. Its finite nontrivial <renormalization-group fixed point> is $(K,L)=(1/3,1/9)$. Higher orders generate additional operators, so the closure is a property of the truncation.
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