Excess number of percolation clusters on the surface of a sphere

Christian D Lorenz and Robert M Ziff

Physica A: Statistical Mechanics and its Applications, 2001, vol. 296, issue 1, 1-8

Abstract: Monte Carlo simulations were performed in order to determine the excess number of clusters b and the average density of clusters nc for the two-dimensional “Swiss cheese” continuum percolation model on a planar L×L system and on the surface of a sphere. The excess number of clusters for the L×L system was confirmed to be a universal quantity with a value b=0.8841 as previously predicted and verified only for lattice percolation. The excess number of clusters on the surface of a sphere was found to have the value b=1.215(1) for discs with the same coverage as the flat critical system. Finally, the average critical density of clusters was calculated for continuum systems as nc=0.04075(5).

Keywords: Percolation; Continuum percolation; Critical phenomenon; Universal quantities (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:296:y:2001:i:1:p:1-8

DOI: 10.1016/S0378-4371(01)00152-2

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