Cluster tomography in percolation
In cluster tomography, we propose measuring the number of clusters N intersected by a line segment of length ℓ across a finite sample. As expected, the leading order of N(ℓ) scales as aℓ, where a depends on microscopic details of the system. However, at criticality, there is often an additional nonl...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2023-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.043218 |
| _version_ | 1797210339169796096 |
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| author | Helen S. Ansell Samuel J. Frank István A. Kovács |
| author_facet | Helen S. Ansell Samuel J. Frank István A. Kovács |
| author_sort | Helen S. Ansell |
| collection | DOAJ |
| description | In cluster tomography, we propose measuring the number of clusters N intersected by a line segment of length ℓ across a finite sample. As expected, the leading order of N(ℓ) scales as aℓ, where a depends on microscopic details of the system. However, at criticality, there is often an additional nonlinearity of the form bln(ℓ), originating from the endpoints of the line segment. By performing large scale Monte Carlo simulations of both two- and three-dimensional percolation, we find that b is universal and depends only on the angles encountered at the endpoints of the line segment intersecting the sample. Our findings are further supported by analytic arguments in two dimensions, building on results in conformal field theory. Being broadly applicable, cluster tomography can be an efficient tool for detecting phase transitions and characterizing the corresponding universality class in classical or quantum systems with a relevant cluster structure. |
| first_indexed | 2024-04-24T10:09:01Z |
| format | Article |
| id | doaj.art-d6f47b936f9947608dc92b91bd37fdac |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:09:01Z |
| publishDate | 2023-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-d6f47b936f9947608dc92b91bd37fdac2024-04-12T17:36:45ZengAmerican Physical SocietyPhysical Review Research2643-15642023-12-015404321810.1103/PhysRevResearch.5.043218Cluster tomography in percolationHelen S. AnsellSamuel J. FrankIstván A. KovácsIn cluster tomography, we propose measuring the number of clusters N intersected by a line segment of length ℓ across a finite sample. As expected, the leading order of N(ℓ) scales as aℓ, where a depends on microscopic details of the system. However, at criticality, there is often an additional nonlinearity of the form bln(ℓ), originating from the endpoints of the line segment. By performing large scale Monte Carlo simulations of both two- and three-dimensional percolation, we find that b is universal and depends only on the angles encountered at the endpoints of the line segment intersecting the sample. Our findings are further supported by analytic arguments in two dimensions, building on results in conformal field theory. Being broadly applicable, cluster tomography can be an efficient tool for detecting phase transitions and characterizing the corresponding universality class in classical or quantum systems with a relevant cluster structure.http://doi.org/10.1103/PhysRevResearch.5.043218 |
| spellingShingle | Helen S. Ansell Samuel J. Frank István A. Kovács Cluster tomography in percolation Physical Review Research |
| title | Cluster tomography in percolation |
| title_full | Cluster tomography in percolation |
| title_fullStr | Cluster tomography in percolation |
| title_full_unstemmed | Cluster tomography in percolation |
| title_short | Cluster tomography in percolation |
| title_sort | cluster tomography in percolation |
| url | http://doi.org/10.1103/PhysRevResearch.5.043218 |
| work_keys_str_mv | AT helensansell clustertomographyinpercolation AT samueljfrank clustertomographyinpercolation AT istvanakovacs clustertomographyinpercolation |