Bond percolation thresholds on Archimedean lattices from critical polynomial roots
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 cal...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.012050 |
| _version_ | 1797211542595305472 |
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| author | Christian R. Scullard Jesper Lykke Jacobsen |
| author_facet | Christian R. Scullard Jesper Lykke Jacobsen |
| author_sort | Christian R. Scullard |
| collection | DOAJ |
| description | 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}=0.52440499916744820(1), whereas the best estimate using standard techniques is p_{c}=0.52440499(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. |
| first_indexed | 2024-04-24T10:28:09Z |
| format | Article |
| id | doaj.art-82d597f1362c4dec950711abca35f9ea |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:28:09Z |
| publishDate | 2020-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-82d597f1362c4dec950711abca35f9ea2024-04-12T16:50:35ZengAmerican Physical SocietyPhysical Review Research2643-15642020-02-012101205010.1103/PhysRevResearch.2.012050Bond percolation thresholds on Archimedean lattices from critical polynomial rootsChristian R. ScullardJesper Lykke JacobsenWe 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}=0.52440499916744820(1), whereas the best estimate using standard techniques is p_{c}=0.52440499(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.http://doi.org/10.1103/PhysRevResearch.2.012050 |
| spellingShingle | Christian R. Scullard Jesper Lykke Jacobsen Bond percolation thresholds on Archimedean lattices from critical polynomial roots Physical Review Research |
| title | Bond percolation thresholds on Archimedean lattices from critical polynomial roots |
| title_full | Bond percolation thresholds on Archimedean lattices from critical polynomial roots |
| title_fullStr | Bond percolation thresholds on Archimedean lattices from critical polynomial roots |
| title_full_unstemmed | Bond percolation thresholds on Archimedean lattices from critical polynomial roots |
| title_short | Bond percolation thresholds on Archimedean lattices from critical polynomial roots |
| title_sort | bond percolation thresholds on archimedean lattices from critical polynomial roots |
| url | http://doi.org/10.1103/PhysRevResearch.2.012050 |
| work_keys_str_mv | AT christianrscullard bondpercolationthresholdsonarchimedeanlatticesfromcriticalpolynomialroots AT jesperlykkejacobsen bondpercolationthresholdsonarchimedeanlatticesfromcriticalpolynomialroots |