2001/02/01 by Christian D. Lorenz, Christian D Lorenz, Robert M. Ziff +1
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1016/s0378-4371(01)00152-2
13 pages, 2 figures
arxiv created 2001/02/01 · openalex publication_date 2001/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 x L system and on the surface of a sphere. The excess number of clusters for the L x 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 nc = 0.0408(1).