High-precision anomalous dimension of 3d percolation from giant cluster slicing - Galvani, Alessandro; Trombettoni, Andrea; Gori, Giacomo (Arxiv, 2021)
We apply the critical geometry approach for bounded critical phenomena [1] to $3d$ percolation. The functional shape of the order parameter profile $φ$ is related via the fractional Yamabe equation to its scaling dimension $Δ_{φ}$. We obtain $Δ_{φ}= 0.4785(7)$ from which the anomalous dimension $η$ is found to be $η=-0.0431(14)$, a value compatible with, and more precise than, its previous direct measurements. A test of hyperscaling is also performed.
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