Inverse percolation by removing straight rigid rods from square lattices

Autores
Ramírez, Lucía Soledad; Centres, Paulo Marcelo; Ramirez Pastor, Antonio Jose
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Numerical simulations and finite-size scaling analysis have beencarried out to study the problem of inverse percolation by removing straightrigid rods from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing straight rigid rods of length k (k-mers) from the surface. The central idea of this paper is based on finding the maximumconcentration of occupied sites (minimum concentration of holes) for whichconnectivity disappears. This particular value of concentration is called theinverse percolation threshold, and determines a well-defined geometrical phasetransition in the system. The results, obtained for k ranging from 2 to 256,showed a nonmonotonic size k dependence for the critical concentration,which rapidly decreases for small particle sizes (1 ⩽k ⩽3 ). Then, it growsfor k = 4, 5 and 6, goes through a maximum at k = 7, and finally decreasesagain and asymptotically converges towards a definite value for large valuesof k. Percolating and non-percolating phases extend to infinity in the space ofthe parameter k and, consequently, the model presents percolation transitionin all ranges of said value. This finding contrasts with the results obtainedin literature for a complementary problem, where straight rigid k-mers arerandomly and irreversibly deposited on a square lattice, and the percolationtransition only exists for values of k ranging between 1 and approximately1.2 × 10^4. The breaking of particle-hole symmetry, a distinctive characteristicof the k-mers statistics, is the source of this asymmetric behavior. Finally, the accurate determination of critical exponents reveals that the model belongs to the same universality class as random percolation regardless of the value of kconsidered.
Fil: Ramírez, Lucía Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; Argentina
Fil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; Argentina
Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; Argentina
Materia
Classical Monte Carlo Simulations
Classical Phase Transitions (Theory)
Phase Diagrams (Theory)
Percolation Problems (Theory)
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14205
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Inverse percolation by removing straight rigid rods from square latticesRamírez, Lucía SoledadCentres, Paulo MarceloRamirez Pastor, Antonio JoseClassical Monte Carlo SimulationsClassical Phase Transitions (Theory)Phase Diagrams (Theory)Percolation Problems (Theory)https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Numerical simulations and finite-size scaling analysis have beencarried out to study the problem of inverse percolation by removing straightrigid rods from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing straight rigid rods of length k (k-mers) from the surface. The central idea of this paper is based on finding the maximumconcentration of occupied sites (minimum concentration of holes) for whichconnectivity disappears. This particular value of concentration is called theinverse percolation threshold, and determines a well-defined geometrical phasetransition in the system. The results, obtained for k ranging from 2 to 256,showed a nonmonotonic size k dependence for the critical concentration,which rapidly decreases for small particle sizes (1 ⩽k ⩽3 ). Then, it growsfor k = 4, 5 and 6, goes through a maximum at k = 7, and finally decreasesagain and asymptotically converges towards a definite value for large valuesof k. Percolating and non-percolating phases extend to infinity in the space ofthe parameter k and, consequently, the model presents percolation transitionin all ranges of said value. This finding contrasts with the results obtainedin literature for a complementary problem, where straight rigid k-mers arerandomly and irreversibly deposited on a square lattice, and the percolationtransition only exists for values of k ranging between 1 and approximately1.2 × 10^4. The breaking of particle-hole symmetry, a distinctive characteristicof the k-mers statistics, is the source of this asymmetric behavior. Finally, the accurate determination of critical exponents reveals that the model belongs to the same universality class as random percolation regardless of the value of kconsidered.Fil: Ramírez, Lucía Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; ArgentinaFil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; ArgentinaFil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; ArgentinaIop Publishing2015-09info: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/11336/14205Ramírez, Lucía Soledad; Centres, Paulo Marcelo; Ramirez Pastor, Antonio Jose; Inverse percolation by removing straight rigid rods from square lattices; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2015; 9-2015; 1-181742-5468enginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1742-5468/2015/09/P09003/metainfo:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2015/09/P09003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:33:56Zoai:ri.conicet.gov.ar:11336/14205instacron: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:34982025-09-29 09:33:56.881CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Inverse percolation by removing straight rigid rods from square lattices
title Inverse percolation by removing straight rigid rods from square lattices
spellingShingle Inverse percolation by removing straight rigid rods from square lattices
Ramírez, Lucía Soledad
Classical Monte Carlo Simulations
Classical Phase Transitions (Theory)
Phase Diagrams (Theory)
Percolation Problems (Theory)
title_short Inverse percolation by removing straight rigid rods from square lattices
title_full Inverse percolation by removing straight rigid rods from square lattices
title_fullStr Inverse percolation by removing straight rigid rods from square lattices
title_full_unstemmed Inverse percolation by removing straight rigid rods from square lattices
title_sort Inverse percolation by removing straight rigid rods from square lattices
dc.creator.none.fl_str_mv Ramírez, Lucía Soledad
Centres, Paulo Marcelo
Ramirez Pastor, Antonio Jose
author Ramírez, Lucía Soledad
author_facet Ramírez, Lucía Soledad
Centres, Paulo Marcelo
Ramirez Pastor, Antonio Jose
author_role author
author2 Centres, Paulo Marcelo
Ramirez Pastor, Antonio Jose
author2_role author
author
dc.subject.none.fl_str_mv Classical Monte Carlo Simulations
Classical Phase Transitions (Theory)
Phase Diagrams (Theory)
Percolation Problems (Theory)
topic Classical Monte Carlo Simulations
Classical Phase Transitions (Theory)
Phase Diagrams (Theory)
Percolation Problems (Theory)
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Numerical simulations and finite-size scaling analysis have beencarried out to study the problem of inverse percolation by removing straightrigid rods from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing straight rigid rods of length k (k-mers) from the surface. The central idea of this paper is based on finding the maximumconcentration of occupied sites (minimum concentration of holes) for whichconnectivity disappears. This particular value of concentration is called theinverse percolation threshold, and determines a well-defined geometrical phasetransition in the system. The results, obtained for k ranging from 2 to 256,showed a nonmonotonic size k dependence for the critical concentration,which rapidly decreases for small particle sizes (1 ⩽k ⩽3 ). Then, it growsfor k = 4, 5 and 6, goes through a maximum at k = 7, and finally decreasesagain and asymptotically converges towards a definite value for large valuesof k. Percolating and non-percolating phases extend to infinity in the space ofthe parameter k and, consequently, the model presents percolation transitionin all ranges of said value. This finding contrasts with the results obtainedin literature for a complementary problem, where straight rigid k-mers arerandomly and irreversibly deposited on a square lattice, and the percolationtransition only exists for values of k ranging between 1 and approximately1.2 × 10^4. The breaking of particle-hole symmetry, a distinctive characteristicof the k-mers statistics, is the source of this asymmetric behavior. Finally, the accurate determination of critical exponents reveals that the model belongs to the same universality class as random percolation regardless of the value of kconsidered.
Fil: Ramírez, Lucía Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; Argentina
Fil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; Argentina
Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina. Universidad Nacional de San Luis; Argentina
description Numerical simulations and finite-size scaling analysis have beencarried out to study the problem of inverse percolation by removing straightrigid rods from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing straight rigid rods of length k (k-mers) from the surface. The central idea of this paper is based on finding the maximumconcentration of occupied sites (minimum concentration of holes) for whichconnectivity disappears. This particular value of concentration is called theinverse percolation threshold, and determines a well-defined geometrical phasetransition in the system. The results, obtained for k ranging from 2 to 256,showed a nonmonotonic size k dependence for the critical concentration,which rapidly decreases for small particle sizes (1 ⩽k ⩽3 ). Then, it growsfor k = 4, 5 and 6, goes through a maximum at k = 7, and finally decreasesagain and asymptotically converges towards a definite value for large valuesof k. Percolating and non-percolating phases extend to infinity in the space ofthe parameter k and, consequently, the model presents percolation transitionin all ranges of said value. This finding contrasts with the results obtainedin literature for a complementary problem, where straight rigid k-mers arerandomly and irreversibly deposited on a square lattice, and the percolationtransition only exists for values of k ranging between 1 and approximately1.2 × 10^4. The breaking of particle-hole symmetry, a distinctive characteristicof the k-mers statistics, is the source of this asymmetric behavior. Finally, the accurate determination of critical exponents reveals that the model belongs to the same universality class as random percolation regardless of the value of kconsidered.
publishDate 2015
dc.date.none.fl_str_mv 2015-09
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/11336/14205
Ramírez, Lucía Soledad; Centres, Paulo Marcelo; Ramirez Pastor, Antonio Jose; Inverse percolation by removing straight rigid rods from square lattices; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2015; 9-2015; 1-18
1742-5468
url http://hdl.handle.net/11336/14205
identifier_str_mv Ramírez, Lucía Soledad; Centres, Paulo Marcelo; Ramirez Pastor, Antonio Jose; Inverse percolation by removing straight rigid rods from square lattices; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2015; 9-2015; 1-18
1742-5468
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1742-5468/2015/09/P09003/meta
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2015/09/P09003
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Iop Publishing
publisher.none.fl_str_mv Iop Publishing
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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