= Bond moving
{title2=$K'=\operatorname{artanh}[\tanh^b(b^{d-1}K)]$}
In the bond-moving-first hypercubic construction with blocking <length> $b$, combine $b^{d-1}$ transverse-equivalent bonds into each link of a surviving $b$-link chain. Summing that chain gives the displayed <Migdal-Kadanoff approximation>. For $b=2$, it becomes $K'=\tfrac12\log\cosh(2^dK)$. The $d=1$ specialization is exact; the higher-dimensional formula is a convention-dependent approximation, not an exact closure of the original hypercubic model.
Back to article page
