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Cluster numbers in percolation | | Stephan Mertens
; Iwan Jensen
; Robert M. Ziff
; | | Date: |
1 Feb 2016 | | Abstract: | We study the number of clusters per site $n(p)$ in lattice percolation on
several systems by high-order series analysis, Monte-Carlo simulation on large
systems, exact enumerations on small systems, and analysis using results from
conformal theory and general percolation theory. We find many new results,
including a precise value $0.017625277368(2)$ for $n(p_c)$ for site percolation
on the triangular lattice, precise measurement of the amplitude of the
singularity $|p-p_c|^{2-alpha}$, and metric scale factors. We make use of the
matching polynomial of Sykes and Essam to find exact relations between
amplitudes for lattices and matching lattices. | | Source: | arXiv, 1602.0644 | | Services: | Forum | Review | PDF | Favorites | |
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