Random site percolation thresholds on square lattice for complex neighborhoods containing sites up to the sixth coordination zone

Krzysztof Malarz

Physica A: Statistical Mechanics and its Applications, 2023, vol. 632, issue P1

Abstract: The site percolation problem is one of the core topics in statistical physics. Evaluation of the percolation threshold, which separates two phases (sometimes described as conducting and insulating), is useful for a range of problems from core condensed matter to interdisciplinary application of statistical physics in epidemiology or other transportation or connectivity problems. In this paper with Newman–Ziff fast Monte Carlo algorithm and finite-size scaling theory the random site percolation thresholds pc for a square lattice with complex neighborhoods containing sites from the sixth coordination zone are computed. Complex neighborhoods are those that contain sites from various coordination zones (which are not necessarily compact). We also present the source codes of the appropriate procedures (written in C) to be replaced in original Newman–Ziff code. Similar to results previously found for the honeycomb lattice, the percolation thresholds for complex neighborhoods on a square lattice follow the power law pc(ζ)∝ζ−γ2 with γ2=0.5454(60), where ζ=∑iziri is the weighted distance of sites in complex neighborhoods (ri and zi are the distance from the central site and the number of sites in the coordination zone i, respectively).

Keywords: Monte Carlo simulation; Finite-size scaling; Non-compact neighborhoods; Universal formula for percolation thresholds (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437123009020
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:632:y:2023:i:p1:s0378437123009020

DOI: 10.1016/j.physa.2023.129347

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().