Back to Search Start Over

Decomposing the percolation backbone reveals novel scaling laws of the current distribution

Authors :
Wagner R. de Sena
José S. Andrade
Hans J. Herrmann
André A. Moreira
Source :
Frontiers in Physics, Vol 11 (2023)
Publication Year :
2023
Publisher :
Frontiers Media S.A., 2023.

Abstract

The distribution of currents on critical percolation clusters is the fundamental quantity describing the transport properties of weakly connected systems. Nevertheless, its finite-size extrapolation is still one of the outstanding open questions concerning disordered media. By hierarchically decomposing the 3-connected components of the backbone, we disclose that the current distribution is determined from two distributions, namely, the one corresponding to the number of bonds in each level and another one corresponding to the factors by which the current is reduced, when going from one level to the next. The first distribution follows a finite-size scaling, while the second is a power law with an exponent consistent with 3/4 in two dimensions. The standard hierarchical model for the backbone is too simple to reproduce this complex scenario. Our new decomposition method of the backbone also allows to calculate much smaller currents than before, attaining a precision of 10−35 and systems of size L = 81922. Moreover, our method is not restricted to electric currents on critical percolation clusters but could also be applied to other transport problems on sparse graphs including fluid flow and car traffic.

Details

Language :
English
ISSN :
2296424X
Volume :
11
Database :
Directory of Open Access Journals
Journal :
Frontiers in Physics
Publication Type :
Academic Journal
Accession number :
edsdoj.51e464dd76fa4ea6b56c52a6a4e60b53
Document Type :
article
Full Text :
https://doi.org/10.3389/fphy.2023.1335339