Analytical solution of the mean field Ising model for finite systems

Autores
Bertoldi, Dalía Surena; Bringa, Eduardo Marcial; Miranda, Enrique Nestor
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Ising model for finite systems, e.g. for clusters of different sizes and crystal lattices, was solved analytically by the mean field approach. The magnetization was calculated from the number of accessible microstates, using the gamma function and its derivatives, unlike the usual solution in the microcanonical which uses the Stirling approximation. We determined a scaling exponent of ~1/3, which shows how the Curie temperature decreases with decreasing nanoparticle size. Moreover, the model predicts the behaviour of surface and core regions and it explains in simple terms several effects previously observed in experiments and Monte Carlo simulations of small magnetic systems.
Fil: Bertoldi, Dalía Surena. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Bringa, Eduardo Marcial. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Miranda, Enrique Nestor. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina
Materia
Ising Model
Clusteer Impact
Microcanonical Solution
Monte Carlo
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:11336/16945
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Analytical solution of the mean field Ising model for finite systemsBertoldi, Dalía SurenaBringa, Eduardo MarcialMiranda, Enrique NestorIsing ModelClusteer ImpactMicrocanonical SolutionMonte Carlohttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The Ising model for finite systems, e.g. for clusters of different sizes and crystal lattices, was solved analytically by the mean field approach. The magnetization was calculated from the number of accessible microstates, using the gamma function and its derivatives, unlike the usual solution in the microcanonical which uses the Stirling approximation. We determined a scaling exponent of ~1/3, which shows how the Curie temperature decreases with decreasing nanoparticle size. Moreover, the model predicts the behaviour of surface and core regions and it explains in simple terms several effects previously observed in experiments and Monte Carlo simulations of small magnetic systems.Fil: Bertoldi, Dalía Surena. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Bringa, Eduardo Marcial. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Miranda, Enrique Nestor. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; ArgentinaIop Publishing2012-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/16945Bertoldi, Dalía Surena; Bringa, Eduardo Marcial; Miranda, Enrique Nestor; Analytical solution of the mean field Ising model for finite systems; Iop Publishing; Journal Of Physics: Condensed Matter; 24; 5-2012; 1-6; 2260040953-8984enginfo:eu-repo/semantics/altIdentifier/doi/10.1088/0953-8984/24/22/226004info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0953-8984/24/22/226004/meta;jsessionid=DEDD350214B74F5306B9837393E9C8B8.ip-10-40-1-105info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:56Zoai:ri.conicet.gov.ar:11336/16945instacron: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 09:50:57.49CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Analytical solution of the mean field Ising model for finite systems
title Analytical solution of the mean field Ising model for finite systems
spellingShingle Analytical solution of the mean field Ising model for finite systems
Bertoldi, Dalía Surena
Ising Model
Clusteer Impact
Microcanonical Solution
Monte Carlo
title_short Analytical solution of the mean field Ising model for finite systems
title_full Analytical solution of the mean field Ising model for finite systems
title_fullStr Analytical solution of the mean field Ising model for finite systems
title_full_unstemmed Analytical solution of the mean field Ising model for finite systems
title_sort Analytical solution of the mean field Ising model for finite systems
dc.creator.none.fl_str_mv Bertoldi, Dalía Surena
Bringa, Eduardo Marcial
Miranda, Enrique Nestor
author Bertoldi, Dalía Surena
author_facet Bertoldi, Dalía Surena
Bringa, Eduardo Marcial
Miranda, Enrique Nestor
author_role author
author2 Bringa, Eduardo Marcial
Miranda, Enrique Nestor
author2_role author
author
dc.subject.none.fl_str_mv Ising Model
Clusteer Impact
Microcanonical Solution
Monte Carlo
topic Ising Model
Clusteer Impact
Microcanonical Solution
Monte Carlo
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The Ising model for finite systems, e.g. for clusters of different sizes and crystal lattices, was solved analytically by the mean field approach. The magnetization was calculated from the number of accessible microstates, using the gamma function and its derivatives, unlike the usual solution in the microcanonical which uses the Stirling approximation. We determined a scaling exponent of ~1/3, which shows how the Curie temperature decreases with decreasing nanoparticle size. Moreover, the model predicts the behaviour of surface and core regions and it explains in simple terms several effects previously observed in experiments and Monte Carlo simulations of small magnetic systems.
Fil: Bertoldi, Dalía Surena. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Bringa, Eduardo Marcial. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Miranda, Enrique Nestor. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina
description The Ising model for finite systems, e.g. for clusters of different sizes and crystal lattices, was solved analytically by the mean field approach. The magnetization was calculated from the number of accessible microstates, using the gamma function and its derivatives, unlike the usual solution in the microcanonical which uses the Stirling approximation. We determined a scaling exponent of ~1/3, which shows how the Curie temperature decreases with decreasing nanoparticle size. Moreover, the model predicts the behaviour of surface and core regions and it explains in simple terms several effects previously observed in experiments and Monte Carlo simulations of small magnetic systems.
publishDate 2012
dc.date.none.fl_str_mv 2012-05
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/11336/16945
Bertoldi, Dalía Surena; Bringa, Eduardo Marcial; Miranda, Enrique Nestor; Analytical solution of the mean field Ising model for finite systems; Iop Publishing; Journal Of Physics: Condensed Matter; 24; 5-2012; 1-6; 226004
0953-8984
url http://hdl.handle.net/11336/16945
identifier_str_mv Bertoldi, Dalía Surena; Bringa, Eduardo Marcial; Miranda, Enrique Nestor; Analytical solution of the mean field Ising model for finite systems; Iop Publishing; Journal Of Physics: Condensed Matter; 24; 5-2012; 1-6; 226004
0953-8984
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/0953-8984/24/22/226004
info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0953-8984/24/22/226004/meta;jsessionid=DEDD350214B74F5306B9837393E9C8B8.ip-10-40-1-105
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
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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score 13.13397

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