A connection between the ice-type model of Linus Pauling and the three-color problem

Detalhes bibliográficos
Autor(a) principal: Silva, Roberto da
Data de Publicação: 2021
Outros Autores: Nakao, Osvaldo Shigueru, Felício, José Roberto Drugovich de
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/218646
Resumo: The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e. colouring a regular graph with coordination equal to 4 (a twodimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of N oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case N → ∞ which is compared with the exact solution by Lieb.
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spelling Silva, Roberto daNakao, Osvaldo ShigueruFelício, José Roberto Drugovich de2021-03-11T04:24:41Z20210143-0807http://hdl.handle.net/10183/218646001122713The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e. colouring a regular graph with coordination equal to 4 (a twodimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of N oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case N → ∞ which is compared with the exact solution by Lieb.application/pdfengEuropean Journal of Physics. Bristol. Vol. 42, no. 2 (Mar. 2021), 025101, 20 p.EntropiaFísica estatísticaMatriz de transferênciaIce-type modelTransfer-matrix methodGraph colouringDidatic alternatives in statistical physicsA connection between the ice-type model of Linus Pauling and the three-color problemEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001122713.pdf.txt001122713.pdf.txtExtracted Texttext/plain43498http://www.lume.ufrgs.br/bitstream/10183/218646/2/001122713.pdf.txt131754fcb239611d89f9ea1a0f9e925aMD52ORIGINAL001122713.pdfTexto completo (inglês)application/pdf1924426http://www.lume.ufrgs.br/bitstream/10183/218646/1/001122713.pdf8cd3164555682c2725beec0022917806MD5110183/2186462021-05-07 05:09:54.66768oai:www.lume.ufrgs.br:10183/218646Repositório InstitucionalPUBhttps://lume.ufrgs.br/oai/requestlume@ufrgs.bropendoar:2021-05-07T08:09:54Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv A connection between the ice-type model of Linus Pauling and the three-color problem
title A connection between the ice-type model of Linus Pauling and the three-color problem
spellingShingle A connection between the ice-type model of Linus Pauling and the three-color problem
Silva, Roberto da
Entropia
Física estatística
Matriz de transferência
Ice-type model
Transfer-matrix method
Graph colouring
Didatic alternatives in statistical physics
title_short A connection between the ice-type model of Linus Pauling and the three-color problem
title_full A connection between the ice-type model of Linus Pauling and the three-color problem
title_fullStr A connection between the ice-type model of Linus Pauling and the three-color problem
title_full_unstemmed A connection between the ice-type model of Linus Pauling and the three-color problem
title_sort A connection between the ice-type model of Linus Pauling and the three-color problem
author Silva, Roberto da
author_facet Silva, Roberto da
Nakao, Osvaldo Shigueru
Felício, José Roberto Drugovich de
author_role author
author2 Nakao, Osvaldo Shigueru
Felício, José Roberto Drugovich de
author2_role author
author
dc.contributor.author.fl_str_mv Silva, Roberto da
Nakao, Osvaldo Shigueru
Felício, José Roberto Drugovich de
dc.subject.por.fl_str_mv Entropia
Física estatística
Matriz de transferência
topic Entropia
Física estatística
Matriz de transferência
Ice-type model
Transfer-matrix method
Graph colouring
Didatic alternatives in statistical physics
dc.subject.eng.fl_str_mv Ice-type model
Transfer-matrix method
Graph colouring
Didatic alternatives in statistical physics
description The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e. colouring a regular graph with coordination equal to 4 (a twodimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of N oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case N → ∞ which is compared with the exact solution by Lieb.
publishDate 2021
dc.date.accessioned.fl_str_mv 2021-03-11T04:24:41Z
dc.date.issued.fl_str_mv 2021
dc.type.driver.fl_str_mv Estrangeiro
info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10183/218646
dc.identifier.issn.pt_BR.fl_str_mv 0143-0807
dc.identifier.nrb.pt_BR.fl_str_mv 001122713
identifier_str_mv 0143-0807
001122713
url http://hdl.handle.net/10183/218646
dc.language.iso.fl_str_mv eng
language eng
dc.relation.ispartof.pt_BR.fl_str_mv European Journal of Physics. Bristol. Vol. 42, no. 2 (Mar. 2021), 025101, 20 p.
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFRGS
instname:Universidade Federal do Rio Grande do Sul (UFRGS)
instacron:UFRGS
instname_str Universidade Federal do Rio Grande do Sul (UFRGS)
instacron_str UFRGS
institution UFRGS
reponame_str Repositório Institucional da UFRGS
collection Repositório Institucional da UFRGS
bitstream.url.fl_str_mv http://www.lume.ufrgs.br/bitstream/10183/218646/2/001122713.pdf.txt
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