Thermodynamics of Small Magnetic Particles

Autores
Vogel, Eugenio; Vargas, Patricio; Saravia, Gonzalo; Valdes, Julio; Ramirez Pastor, Antonio Jose; Centres, Paulo Marcelo
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present paper, we discuss the interpretation of some of the results of the thermodynamics in the case of very small systems. Most of the usual statistical physics is done for systems with a huge number of elements in what is called the thermodynamic limit, but not all of the approximations done for those conditions can be extended to all properties in the case of objects with less than a thousand elements. The starting point is the Ising model in two dimensions (2D) where an analytic solution exits, which allows validating the numerical techniques used in the present article. From there on, we introduce several variations bearing in mind the small systems such as the nanoscopic or even subnanoscopic particles, which are nowadays produced for several applications. Magnetization is the main property investigated aimed for two singular possible devices. The size of the systems (number of magnetic sites) is decreased so as to appreciate the departure from the results valid in the thermodynamic limit; periodic boundary conditions are eliminated to approach the reality of small particles; 1D, 2D and 3D systems are examined to appreciate the differences established by dimensionality is this small world; upon diluting the lattices, the effect of coordination number (bonding) is also explored; since the 2D Ising model is equivalent to the clock model with q=2 degrees of freedom, we combine previous results with the supplementary degrees of freedom coming from the variation of q up to q=20. Most of the previous results are numeric; however, for the case of a very small system, we obtain the exact partition function to compare with the conclusions coming from our numerical results. Conclusions can be summarized in the following way: the laws of thermodynamics remain the same, but the interpretation of the results, averages and numerical treatments need special care for systems with less than about a thousand constituents, and this might need to be adapted for different properties or devices.
Fil: Vogel, Eugenio. Universidad de La Frontera; Chile. Center for the Development of Nanoscience and Nanotechnology; Chile
Fil: Vargas, Patricio. Center for the Development of Nanoscience and Nanotechnology; Chile. Universidad Técnica Federico Santa María; Chile
Fil: Saravia, Gonzalo. Universidad de La Frontera; Chile
Fil: Valdes, Julio. Universidad de La Frontera; Chile
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
Materia
SMALL SYSTEMS
THERMODYNAMICS
MAGNETIZATION
DILUTION
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:11336/63862
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/63862
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Thermodynamics of Small Magnetic ParticlesVogel, EugenioVargas, PatricioSaravia, GonzaloValdes, JulioRamirez Pastor, Antonio JoseCentres, Paulo MarceloSMALL SYSTEMSTHERMODYNAMICSMAGNETIZATIONDILUTIONhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In the present paper, we discuss the interpretation of some of the results of the thermodynamics in the case of very small systems. Most of the usual statistical physics is done for systems with a huge number of elements in what is called the thermodynamic limit, but not all of the approximations done for those conditions can be extended to all properties in the case of objects with less than a thousand elements. The starting point is the Ising model in two dimensions (2D) where an analytic solution exits, which allows validating the numerical techniques used in the present article. From there on, we introduce several variations bearing in mind the small systems such as the nanoscopic or even subnanoscopic particles, which are nowadays produced for several applications. Magnetization is the main property investigated aimed for two singular possible devices. The size of the systems (number of magnetic sites) is decreased so as to appreciate the departure from the results valid in the thermodynamic limit; periodic boundary conditions are eliminated to approach the reality of small particles; 1D, 2D and 3D systems are examined to appreciate the differences established by dimensionality is this small world; upon diluting the lattices, the effect of coordination number (bonding) is also explored; since the 2D Ising model is equivalent to the clock model with q=2 degrees of freedom, we combine previous results with the supplementary degrees of freedom coming from the variation of q up to q=20. Most of the previous results are numeric; however, for the case of a very small system, we obtain the exact partition function to compare with the conclusions coming from our numerical results. Conclusions can be summarized in the following way: the laws of thermodynamics remain the same, but the interpretation of the results, averages and numerical treatments need special care for systems with less than about a thousand constituents, and this might need to be adapted for different properties or devices.Fil: Vogel, Eugenio. Universidad de La Frontera; Chile. Center for the Development of Nanoscience and Nanotechnology; ChileFil: Vargas, Patricio. Center for the Development of Nanoscience and Nanotechnology; Chile. Universidad Técnica Federico Santa María; ChileFil: Saravia, Gonzalo. Universidad de La Frontera; ChileFil: Valdes, Julio. Universidad de La Frontera; ChileFil: 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"; ArgentinaMolecular Diversity Preservation International2017-09-15info: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/11336/63862Vogel, Eugenio; Vargas, Patricio; Saravia, Gonzalo; Valdes, Julio; Ramirez Pastor, Antonio Jose; et al.; Thermodynamics of Small Magnetic Particles; Molecular Diversity Preservation International; Entropy; 19; 9; 15-9-2017; 1-201099-4300CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3390/e19090499info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/19/9/499info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:40:45Zoai:ri.conicet.gov.ar:11336/63862instacron: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 09:40:45.663CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Thermodynamics of Small Magnetic Particles
title Thermodynamics of Small Magnetic Particles
spellingShingle Thermodynamics of Small Magnetic Particles
Vogel, Eugenio
SMALL SYSTEMS
THERMODYNAMICS
MAGNETIZATION
DILUTION
title_short Thermodynamics of Small Magnetic Particles
title_full Thermodynamics of Small Magnetic Particles
title_fullStr Thermodynamics of Small Magnetic Particles
title_full_unstemmed Thermodynamics of Small Magnetic Particles
title_sort Thermodynamics of Small Magnetic Particles
dc.creator.none.fl_str_mv Vogel, Eugenio
Vargas, Patricio
Saravia, Gonzalo
Valdes, Julio
Ramirez Pastor, Antonio Jose
Centres, Paulo Marcelo
author Vogel, Eugenio
author_facet Vogel, Eugenio
Vargas, Patricio
Saravia, Gonzalo
Valdes, Julio
Ramirez Pastor, Antonio Jose
Centres, Paulo Marcelo
author_role author
author2 Vargas, Patricio
Saravia, Gonzalo
Valdes, Julio
Ramirez Pastor, Antonio Jose
Centres, Paulo Marcelo
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv SMALL SYSTEMS
THERMODYNAMICS
MAGNETIZATION
DILUTION
topic SMALL SYSTEMS
THERMODYNAMICS
MAGNETIZATION
DILUTION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the present paper, we discuss the interpretation of some of the results of the thermodynamics in the case of very small systems. Most of the usual statistical physics is done for systems with a huge number of elements in what is called the thermodynamic limit, but not all of the approximations done for those conditions can be extended to all properties in the case of objects with less than a thousand elements. The starting point is the Ising model in two dimensions (2D) where an analytic solution exits, which allows validating the numerical techniques used in the present article. From there on, we introduce several variations bearing in mind the small systems such as the nanoscopic or even subnanoscopic particles, which are nowadays produced for several applications. Magnetization is the main property investigated aimed for two singular possible devices. The size of the systems (number of magnetic sites) is decreased so as to appreciate the departure from the results valid in the thermodynamic limit; periodic boundary conditions are eliminated to approach the reality of small particles; 1D, 2D and 3D systems are examined to appreciate the differences established by dimensionality is this small world; upon diluting the lattices, the effect of coordination number (bonding) is also explored; since the 2D Ising model is equivalent to the clock model with q=2 degrees of freedom, we combine previous results with the supplementary degrees of freedom coming from the variation of q up to q=20. Most of the previous results are numeric; however, for the case of a very small system, we obtain the exact partition function to compare with the conclusions coming from our numerical results. Conclusions can be summarized in the following way: the laws of thermodynamics remain the same, but the interpretation of the results, averages and numerical treatments need special care for systems with less than about a thousand constituents, and this might need to be adapted for different properties or devices.
Fil: Vogel, Eugenio. Universidad de La Frontera; Chile. Center for the Development of Nanoscience and Nanotechnology; Chile
Fil: Vargas, Patricio. Center for the Development of Nanoscience and Nanotechnology; Chile. Universidad Técnica Federico Santa María; Chile
Fil: Saravia, Gonzalo. Universidad de La Frontera; Chile
Fil: Valdes, Julio. Universidad de La Frontera; Chile
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
description In the present paper, we discuss the interpretation of some of the results of the thermodynamics in the case of very small systems. Most of the usual statistical physics is done for systems with a huge number of elements in what is called the thermodynamic limit, but not all of the approximations done for those conditions can be extended to all properties in the case of objects with less than a thousand elements. The starting point is the Ising model in two dimensions (2D) where an analytic solution exits, which allows validating the numerical techniques used in the present article. From there on, we introduce several variations bearing in mind the small systems such as the nanoscopic or even subnanoscopic particles, which are nowadays produced for several applications. Magnetization is the main property investigated aimed for two singular possible devices. The size of the systems (number of magnetic sites) is decreased so as to appreciate the departure from the results valid in the thermodynamic limit; periodic boundary conditions are eliminated to approach the reality of small particles; 1D, 2D and 3D systems are examined to appreciate the differences established by dimensionality is this small world; upon diluting the lattices, the effect of coordination number (bonding) is also explored; since the 2D Ising model is equivalent to the clock model with q=2 degrees of freedom, we combine previous results with the supplementary degrees of freedom coming from the variation of q up to q=20. Most of the previous results are numeric; however, for the case of a very small system, we obtain the exact partition function to compare with the conclusions coming from our numerical results. Conclusions can be summarized in the following way: the laws of thermodynamics remain the same, but the interpretation of the results, averages and numerical treatments need special care for systems with less than about a thousand constituents, and this might need to be adapted for different properties or devices.
publishDate 2017
dc.date.none.fl_str_mv 2017-09-15
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/11336/63862
Vogel, Eugenio; Vargas, Patricio; Saravia, Gonzalo; Valdes, Julio; Ramirez Pastor, Antonio Jose; et al.; Thermodynamics of Small Magnetic Particles; Molecular Diversity Preservation International; Entropy; 19; 9; 15-9-2017; 1-20
1099-4300
CONICET Digital
CONICET
url http://hdl.handle.net/11336/63862
identifier_str_mv Vogel, Eugenio; Vargas, Patricio; Saravia, Gonzalo; Valdes, Julio; Ramirez Pastor, Antonio Jose; et al.; Thermodynamics of Small Magnetic Particles; Molecular Diversity Preservation International; Entropy; 19; 9; 15-9-2017; 1-20
1099-4300
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3390/e19090499
info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/19/9/499
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 Molecular Diversity Preservation International
publisher.none.fl_str_mv Molecular Diversity Preservation International
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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