Fast Monte Carlo algorithm for site or bond percolation.

By Mark Newman, Robert M. Ziff. Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

423 citations recorded by the source corpus.

We describe in detail an efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site percolation on the square lattice, the stretched exponential behavior of spanning probabilities away from the critical point, and the size of the giant component for site percolation on random graphs.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/81fd99fa6344cb5a307ce2823479cc39ed88d081

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In Condensed Matter Physics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Electrical properties of single wall carbon nanotube reinforced polyimide composites (2003, methodology): “The cluster structures were handled using a modified version of the efficient tree-based union/find algorithm [25].”
Piezoresistive Strain Sensors Made from Carbon Nanotubes Based Polymer Nanocomposites (2011, methodology): “The union/finding algorithm [72] was adopted to detect the first complete conductive path spanning the 3D element (red CNTs in Figure 3), and the percolation threshold could then be determined from the total volume of capped cylinder CNTs and the volume of the representative element.”
Evolution of networks (2001, methodology): “s are possible only for the simplest degree distributions but numerics is easily applicable [61]. The results may be also checked by simulation using, e.g., eﬃcient algorithm for percolation problems [202]. In the same paper [61], one can ﬁnd another generalization of this theory to the case of undi”
The Anatomy of the Facebook Social Graph (2011, methodology): “cy for each neighborhood size are therefore empirical percentiles from this sample population of 5,000 users. To analyze the component structure of the network, we used the Newman-Zipf (NZ) algorithm [47]. The NZ algorithm, a type of Union-Find algorithm with path compression, records component stru”
Effect of fabrication process on electrical properties of polymer/multi-wall carbon nanotube nanocomposites (2008, methodology): “The tree-like union/find algorithm [25] was adopted to detect the first complete conducting path connecting two sides of 3D cube (marked in Fig.”
Connectivity metrics for subsurface flow and transport (2013, methodology): “The details of an efficient computer implementation of the calculation of C(x) from I(x) are given for example in Hoshen and Kopelman [97] or Newman and Ziff [98] (see Appendix for additional information about available codes).”