Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevE.67.066108 http://hdl.handle.net/11449/130465 |
Resumo: | We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations. |
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Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagramsCalculationsConvergence of numerical methodsCorrelation methodsEigenvalues and eigenfunctionsGraph theoryMagnetic fieldsMathematical modelsRandom processesTemperatureFeynman diagramIsing modelRandom graphThree-state Potts modelTwo-state Potts modelYang-Lee zerosStatistical mechanicsWe present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.Faculdade de Tecnologia de Sao Paulo CEETEPS-UNESP Praca Fernando Prestes, 30, 01124-060 Sao Paulo, Sao PauloUNESP Campus de Guaratingueta DFQ, Avenida Dr. Ariberto Pereira da Cunh, 12516-410 Guaratingueta, Sao PauloFaculdade de Tecnologia de Sao Paulo CEETEPS-UNESP Praca Fernando Prestes, 30, 01124-060 Sao Paulo, Sao PauloUNESP Campus de Guaratingueta DFQ, Avenida Dr. Ariberto Pereira da Cunh, 12516-410 Guaratingueta, Sao PauloAmer Physical SocUniversidade Estadual Paulista (Unesp)Faculdade de Tecnologia de São Paulo (CEETEPS)Albuquerque, Luiz C. de [UNESP]Dalmazi, D. [UNESP]2014-05-20T15:24:41Z2014-05-20T15:24:41Z2003-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article7application/pdfhttp://dx.doi.org/10.1103/PhysRevE.67.066108Physical Review E. College Pk: Amer Physical Soc, v. 67, n. 6, 7 p., 2003.1063-651X1539-3755http://hdl.handle.net/11449/13046510.1103/PhysRevE.67.066108WOS:0001840850000202-s2.0-427491084352-s2.0-42749108435.pdf8279393876415608Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Einfo:eu-repo/semantics/openAccess2024-01-09T06:31:56Zoai:repositorio.unesp.br:11449/130465Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-05-23T20:17:06.355038Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams |
title |
Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams |
spellingShingle |
Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams Albuquerque, Luiz C. de [UNESP] Calculations Convergence of numerical methods Correlation methods Eigenvalues and eigenfunctions Graph theory Magnetic fields Mathematical models Random processes Temperature Feynman diagram Ising model Random graph Three-state Potts model Two-state Potts model Yang-Lee zeros Statistical mechanics |
title_short |
Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams |
title_full |
Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams |
title_fullStr |
Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams |
title_full_unstemmed |
Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams |
title_sort |
Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams |
author |
Albuquerque, Luiz C. de [UNESP] |
author_facet |
Albuquerque, Luiz C. de [UNESP] Dalmazi, D. [UNESP] |
author_role |
author |
author2 |
Dalmazi, D. [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Faculdade de Tecnologia de São Paulo (CEETEPS) |
dc.contributor.author.fl_str_mv |
Albuquerque, Luiz C. de [UNESP] Dalmazi, D. [UNESP] |
dc.subject.por.fl_str_mv |
Calculations Convergence of numerical methods Correlation methods Eigenvalues and eigenfunctions Graph theory Magnetic fields Mathematical models Random processes Temperature Feynman diagram Ising model Random graph Three-state Potts model Two-state Potts model Yang-Lee zeros Statistical mechanics |
topic |
Calculations Convergence of numerical methods Correlation methods Eigenvalues and eigenfunctions Graph theory Magnetic fields Mathematical models Random processes Temperature Feynman diagram Ising model Random graph Three-state Potts model Two-state Potts model Yang-Lee zeros Statistical mechanics |
description |
We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations. |
publishDate |
2003 |
dc.date.none.fl_str_mv |
2003-06-01 2014-05-20T15:24:41Z 2014-05-20T15:24:41Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1103/PhysRevE.67.066108 Physical Review E. College Pk: Amer Physical Soc, v. 67, n. 6, 7 p., 2003. 1063-651X 1539-3755 http://hdl.handle.net/11449/130465 10.1103/PhysRevE.67.066108 WOS:000184085000020 2-s2.0-42749108435 2-s2.0-42749108435.pdf 8279393876415608 |
url |
http://dx.doi.org/10.1103/PhysRevE.67.066108 http://hdl.handle.net/11449/130465 |
identifier_str_mv |
Physical Review E. College Pk: Amer Physical Soc, v. 67, n. 6, 7 p., 2003. 1063-651X 1539-3755 10.1103/PhysRevE.67.066108 WOS:000184085000020 2-s2.0-42749108435 2-s2.0-42749108435.pdf 8279393876415608 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review E |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
7 application/pdf |
dc.publisher.none.fl_str_mv |
Amer Physical Soc |
publisher.none.fl_str_mv |
Amer Physical Soc |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803045661008986112 |