High-precision anomalous dimension of 3d percolation from giant cluster slicing
We apply the critical geometry approach for bounded critical phenomena [1] to $3d$ percolation. The functional shape of the order parameter profile $\phi$ is related via the fractional Yamabe equation to its scaling dimension $\Delta_{\phi}$. We obtain $\Delta_{\phi}= 0.4785(7)$ from which the anoma...
Gespeichert in:
| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
25 Oct 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-11 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2110.13232
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| Verfasserangaben: | Alessandro Galvani, Andrea Trombettoni, and Giacomo Gori |
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| 520 | |a We apply the critical geometry approach for bounded critical phenomena [1] to $3d$ percolation. The functional shape of the order parameter profile $\phi$ is related via the fractional Yamabe equation to its scaling dimension $\Delta_{\phi}$. We obtain $\Delta_{\phi}= 0.4785(7)$ from which the anomalous dimension $\eta$ is found to be $\eta=-0.0431(14)$, a value compatible with, and more precise than, its previous direct measurements. A test of hyperscaling is also performed. | ||
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