High-precision anomalous dimension of 3d percolation from giant cluster slicing

• Verfasst von: Galvani, Alessandro [VerfasserIn]
• Verfasst von: Trombettoni, Andrea [VerfasserIn]
• Verfasst von: Gori, Giacomo [VerfasserIn]
• Titel: High-precision anomalous dimension of 3d percolation from giant cluster slicing
• Verf.angabe: Alessandro Galvani, Andrea Trombettoni, and Giacomo Gori
• E-Jahr: 2021
• Jahr: 25 Oct 2021
• Umfang: 11 S.
• Fussnoten: Gesehen am 07.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), Artikel-ID 2110.13232, Seite 1-11
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Condensed Matter - Statistical Mechanics
• K10plus-PPN: 180442675X

Abstract

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.