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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/117074

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spelling 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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