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Title: Bond percolation thresholds on Archimedean lattices from critical polynomial roots

Abstract

We present percolation thresholds calculated numerically with the eigenvalue formulation of the method of critical polynomials; developed in the last few years, it has already proven to be orders of magnitude more accurate than traditional techniques. Here, we report the result of large parallel calculations to produce what we believe may become the reference values of bond percolation thresholds on the Archimedean lattices for years to come. For example, for the kagome lattice we find p c= 0.524 404 999 167 448 20 (1) , whereas the best estimate using standard techniques is p c= 0.524 404 99 (2) . We further provide strong evidence that there are two classes of lattices: one for which the first three scaling exponents characterizing the finite-size corrections to p c are Δ = 6, 7, 8 , and another for which Δ = 4, 6, 8. We discuss the open questions related to the method, such as the full scaling law, as well as its potential for determining the critical points of other models.

Authors:
; ORCiD logo
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1602370
Alternate Identifier(s):
OSTI ID: 1670554
Report Number(s):
LLNL-JRNL-795621
Journal ID: ISSN 2643-1564; PPRHAI; 012050
Grant/Contract Number:  
AC52-07NA27344; 19-DR-013
Resource Type:
Journal Article: Published Article
Journal Name:
Physical Review Research
Additional Journal Information:
Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 1; Journal ID: ISSN 2643-1564
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL PROTECTION

Citation Formats

Scullard, Christian R., and Jacobsen, Jesper Lykke. Bond percolation thresholds on Archimedean lattices from critical polynomial roots. United States: N. p., 2020. Web. doi:10.1103/PhysRevResearch.2.012050.
Scullard, Christian R., & Jacobsen, Jesper Lykke. Bond percolation thresholds on Archimedean lattices from critical polynomial roots. United States. https://doi.org/10.1103/PhysRevResearch.2.012050
Scullard, Christian R., and Jacobsen, Jesper Lykke. Fri . "Bond percolation thresholds on Archimedean lattices from critical polynomial roots". United States. https://doi.org/10.1103/PhysRevResearch.2.012050.
@article{osti_1602370,
title = {Bond percolation thresholds on Archimedean lattices from critical polynomial roots},
author = {Scullard, Christian R. and Jacobsen, Jesper Lykke},
abstractNote = {We present percolation thresholds calculated numerically with the eigenvalue formulation of the method of critical polynomials; developed in the last few years, it has already proven to be orders of magnitude more accurate than traditional techniques. Here, we report the result of large parallel calculations to produce what we believe may become the reference values of bond percolation thresholds on the Archimedean lattices for years to come. For example, for the kagome lattice we find pc= 0.524 404 999 167 448 20 (1) , whereas the best estimate using standard techniques is pc= 0.524 404 99 (2) . We further provide strong evidence that there are two classes of lattices: one for which the first three scaling exponents characterizing the finite-size corrections to pc are Δ = 6, 7, 8 , and another for which Δ = 4, 6, 8. We discuss the open questions related to the method, such as the full scaling law, as well as its potential for determining the critical points of other models.},
doi = {10.1103/PhysRevResearch.2.012050},
url = {https://www.osti.gov/biblio/1602370}, journal = {Physical Review Research},
issn = {2643-1564},
number = 1,
volume = 2,
place = {United States},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at https://doi.org/10.1103/PhysRevResearch.2.012050

Figures / Tables:

FIG. 1 FIG. 1: The eleven Archimedean lattices.

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Works referenced in this record:

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    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.