Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study
- Autores
- Ramirez Pastor, Antonio Jose; Centres, Paulo Marcelo; Vogel, Eugenio; Valdés, J. F.
- Año de publicación
- 2019
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Percolation and jamming of k×k square tiles (k2-mers) deposited on square lattices have been studied by numerical simulations complemented with finite-size scaling theory and exact enumeration of configurations for small systems. The k2-mers were irreversibly deposited into square lattices of sizes L×L with L/k ranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θj,k was determined for a wide range of k values (2≤k≤100 with many intermediate k values to allow a fine scaling analysis). θj,k exhibits a decreasing behavior with increasing k, being θj,k= 0.5623(3) the limit value for large k2-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent νj was measured, being νj≈1. On the other hand, the obtained results for the percolation threshold θc,k showed that θc,k is an increasing function of k in the range 1≤k≤3. For k≥4, all jammed configurations are nonpercolating states and, consequently, the percolation phase transition disappears. An explanation for this phenomenon is offered in terms of the rapid increase with k of the number of surrounding occupied sites needed to reach percolation, which gets larger than the sufficient number of occupied sites to define jamming. In the case of k=2 and 3, the percolation thresholds are θc,k=2(-)=0.60355(8) and θc,k=3=0.63110(9). Our results significantly improve the previously reported values of θc,k=2Naka=0.601(7) and θc,k=3Naka=0.621(6) [Nakamura, Phys. Rev. A 36, 2384 (1987)0556-279110.1103/PhysRevA.36.2384]. In parallel, a comparison with previous results for jamming on these systems is also done. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the ordinary random percolation, regardless of the size k considered.
Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Fil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Fil: Vogel, Eugenio. Universidad de La Frontera; Chile. Centro, el Centro para el Desarrollo de la Nanociencia y la Nanotecnología; Chile
Fil: Valdés, J. F.. Universidad de La Frontera; Chile - Materia
-
PERCOLATION
MONTE CARLO
SQUARE LATTICES - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/117074
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Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation studyRamirez Pastor, Antonio JoseCentres, Paulo MarceloVogel, EugenioValdés, J. F.PERCOLATIONMONTE CARLOSQUARE LATTICEShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Percolation and jamming of k×k square tiles (k2-mers) deposited on square lattices have been studied by numerical simulations complemented with finite-size scaling theory and exact enumeration of configurations for small systems. The k2-mers were irreversibly deposited into square lattices of sizes L×L with L/k ranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θj,k was determined for a wide range of k values (2≤k≤100 with many intermediate k values to allow a fine scaling analysis). θj,k exhibits a decreasing behavior with increasing k, being θj,k= 0.5623(3) the limit value for large k2-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent νj was measured, being νj≈1. On the other hand, the obtained results for the percolation threshold θc,k showed that θc,k is an increasing function of k in the range 1≤k≤3. For k≥4, all jammed configurations are nonpercolating states and, consequently, the percolation phase transition disappears. An explanation for this phenomenon is offered in terms of the rapid increase with k of the number of surrounding occupied sites needed to reach percolation, which gets larger than the sufficient number of occupied sites to define jamming. In the case of k=2 and 3, the percolation thresholds are θc,k=2(-)=0.60355(8) and θc,k=3=0.63110(9). Our results significantly improve the previously reported values of θc,k=2Naka=0.601(7) and θc,k=3Naka=0.621(6) [Nakamura, Phys. Rev. A 36, 2384 (1987)0556-279110.1103/PhysRevA.36.2384]. In parallel, a comparison with previous results for jamming on these systems is also done. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the ordinary random percolation, regardless of the size k considered.Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Vogel, Eugenio. Universidad de La Frontera; Chile. Centro, el Centro para el Desarrollo de la Nanociencia y la Nanotecnología; ChileFil: Valdés, J. F.. Universidad de La Frontera; ChileAmerican Physical Society2019-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/117074Ramirez Pastor, Antonio Jose; Centres, Paulo Marcelo; Vogel, Eugenio; Valdés, J. F.; Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 99; 4; 4-2019; 1-111539-3755CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.99.042131info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.042131info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1905.11438info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:53:56Zoai:ri.conicet.gov.ar:11336/117074instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:53:57.189CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study |
title |
Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study |
spellingShingle |
Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study Ramirez Pastor, Antonio Jose PERCOLATION MONTE CARLO SQUARE LATTICES |
title_short |
Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study |
title_full |
Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study |
title_fullStr |
Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study |
title_full_unstemmed |
Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study |
title_sort |
Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study |
dc.creator.none.fl_str_mv |
Ramirez Pastor, Antonio Jose Centres, Paulo Marcelo Vogel, Eugenio Valdés, J. F. |
author |
Ramirez Pastor, Antonio Jose |
author_facet |
Ramirez Pastor, Antonio Jose Centres, Paulo Marcelo Vogel, Eugenio Valdés, J. F. |
author_role |
author |
author2 |
Centres, Paulo Marcelo Vogel, Eugenio Valdés, J. F. |
author2_role |
author author author |
dc.subject.none.fl_str_mv |
PERCOLATION MONTE CARLO SQUARE LATTICES |
topic |
PERCOLATION MONTE CARLO SQUARE LATTICES |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Percolation and jamming of k×k square tiles (k2-mers) deposited on square lattices have been studied by numerical simulations complemented with finite-size scaling theory and exact enumeration of configurations for small systems. The k2-mers were irreversibly deposited into square lattices of sizes L×L with L/k ranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θj,k was determined for a wide range of k values (2≤k≤100 with many intermediate k values to allow a fine scaling analysis). θj,k exhibits a decreasing behavior with increasing k, being θj,k= 0.5623(3) the limit value for large k2-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent νj was measured, being νj≈1. On the other hand, the obtained results for the percolation threshold θc,k showed that θc,k is an increasing function of k in the range 1≤k≤3. For k≥4, all jammed configurations are nonpercolating states and, consequently, the percolation phase transition disappears. An explanation for this phenomenon is offered in terms of the rapid increase with k of the number of surrounding occupied sites needed to reach percolation, which gets larger than the sufficient number of occupied sites to define jamming. In the case of k=2 and 3, the percolation thresholds are θc,k=2(-)=0.60355(8) and θc,k=3=0.63110(9). Our results significantly improve the previously reported values of θc,k=2Naka=0.601(7) and θc,k=3Naka=0.621(6) [Nakamura, Phys. Rev. A 36, 2384 (1987)0556-279110.1103/PhysRevA.36.2384]. In parallel, a comparison with previous results for jamming on these systems is also done. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the ordinary random percolation, regardless of the size k considered. Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina Fil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina Fil: Vogel, Eugenio. Universidad de La Frontera; Chile. Centro, el Centro para el Desarrollo de la Nanociencia y la Nanotecnología; Chile Fil: Valdés, J. F.. Universidad de La Frontera; Chile |
description |
Percolation and jamming of k×k square tiles (k2-mers) deposited on square lattices have been studied by numerical simulations complemented with finite-size scaling theory and exact enumeration of configurations for small systems. The k2-mers were irreversibly deposited into square lattices of sizes L×L with L/k ranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θj,k was determined for a wide range of k values (2≤k≤100 with many intermediate k values to allow a fine scaling analysis). θj,k exhibits a decreasing behavior with increasing k, being θj,k= 0.5623(3) the limit value for large k2-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent νj was measured, being νj≈1. On the other hand, the obtained results for the percolation threshold θc,k showed that θc,k is an increasing function of k in the range 1≤k≤3. For k≥4, all jammed configurations are nonpercolating states and, consequently, the percolation phase transition disappears. An explanation for this phenomenon is offered in terms of the rapid increase with k of the number of surrounding occupied sites needed to reach percolation, which gets larger than the sufficient number of occupied sites to define jamming. In the case of k=2 and 3, the percolation thresholds are θc,k=2(-)=0.60355(8) and θc,k=3=0.63110(9). Our results significantly improve the previously reported values of θc,k=2Naka=0.601(7) and θc,k=3Naka=0.621(6) [Nakamura, Phys. Rev. A 36, 2384 (1987)0556-279110.1103/PhysRevA.36.2384]. In parallel, a comparison with previous results for jamming on these systems is also done. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the ordinary random percolation, regardless of the size k considered. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-04 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/117074 Ramirez Pastor, Antonio Jose; Centres, Paulo Marcelo; Vogel, Eugenio; Valdés, J. F.; Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 99; 4; 4-2019; 1-11 1539-3755 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/117074 |
identifier_str_mv |
Ramirez Pastor, Antonio Jose; Centres, Paulo Marcelo; Vogel, Eugenio; Valdés, J. F.; Jamming and percolation for deposition of k2-mers on square lattices: A Monte Carlo simulation study; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 99; 4; 4-2019; 1-11 1539-3755 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.99.042131 info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.042131 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1905.11438 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
American Physical Society |
publisher.none.fl_str_mv |
American Physical Society |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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1842269258539597825 |
score |
13.13397 |