Determination of the percolation critical exponent as measure of dimension
Abstract
The critical exponent β related to the percolation probability describes the dimensionality of a specific lattice topology. The accurate determination of β will aid in distinguishing different universality classes. This work describes the fine tuning of the Sigma method developed previously by the authors in obtaining β. The approach uses the log-log plot of the percolation probability versus the difference of the occupation probability and the percolation threshold. Considering a symmetric distribution of points about the midpoint of this plot yields the β with (1) the lowest standard deviation and (2) the appropriate asymptotic behavior for both one and two-dimensional lattices.
Downloads
Published
Issue
Section
License
By submitting their manuscript to the Samahang Pisika ng Pilipinas (SPP) for consideration, the Authors warrant that their work is original, does not infringe on existing copyrights, and is not under active consideration for publication elsewhere.
Upon acceptance of their manuscript, the Authors further agree to grant SPP the non-exclusive, worldwide, and royalty-free rights to record, edit, copy, reproduce, publish, distribute, and use all or part of the manuscript for any purpose, in any media now existing or developed in the future, either individually or as part of a collection.
All other associated economic and moral rights as granted by the Intellectual Property Code of the Philippines are maintained by the Authors.
