= Blocking kernel
{title2=$\sum_{\sigma'}K_b(\sigma',\sigma)=1$}
A blocking kernel assigns a conditional probability to coarse configurations given microscopic configurations. Multiplying each microscopic Boltzmann weight by the kernel and summing over microscopic configurations defines the coarse Hamiltonian. The normalization preserves the <partition function> exactly when the coarse operator space is not truncated. In $D$ dimensions a blocking factor $b$ changes the lattice spacing to $ba$ and the number of sites to $N/b^D$. Generated interactions and additive constants must be retained for the transformation to remain exact.
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