High-precision anomalous dimension of three-dimensional percolation and spatial profile of the critical giant cluster

Year: 2022

Authors: Galvani A., Trombettoni A., Gori G.

Autors Affiliation: SISSA, Sez Trieste, Via Bonomea 265, I-34136 Sissa, Trieste, Italy; INFN, Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy; Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; CNR IOM DEMOCRITOS Simulat Ctr, Via Bonomea 265, I-34136 Trieste, Italy; SISSA, Via Bonomea 265, I-34136 Trieste, Italy.

Abstract: In three-dimensional percolation, we apply and test the critical geometry approach for bounded critical phenomena based on the fractional Yamabe equation. The method predicts the functional shape of the order parameter profile o, which is obtained by raising the solution of the Yamabe equation to the scaling dimension Ao. The latter can be fixed from outcomes of numerical simulations, from which we obtain Ao = 0.47846(71) and the corresponding value of the anomalous dimension eta = -0.0431(14). The comparison with values of eta determined by using scaling relations is discussed. A test of hyperscaling is also performed.

Journal/Review: PHYSICAL REVIEW E

Volume: 106 (6)      Pages from: 64111-1  to: 64111-8

More Information: G.G. is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster) . G.G. also acknowledges QSTAR for hospitality during completion of this work.
KeyWords: Molecular-size Distribution; Monte-carlo; Renormalization-group; Scaling Corrections; Phase-transitions; Bond Percolation; Site Percolation; Model; Universality; Threshold
DOI: 10.1103/PhysRevE.106.064111