= Upper critical dimension of percolation
{title2=$d_c=6$}
Six is the predicted boundary for ordinary short-range <percolation> to have <mean-field percolation exponents>, with logarithmic corrections expected at the boundary. If the Fourier connectivity has leading small-momentum behavior $|k|^{-2}$, the triangle integral scales as $\int_0^\varepsilon r^{d-7}\,dr$, finite exactly for $d>6$. This is a scaling argument; rigorous nearest-neighbor results require their own dimensional hypotheses.
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