Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at crit...

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Detalles Bibliográficos
Autores: Fernández Pérez, Luis Antonio, Gordillo Guerrero, A., Martín Mayor, Víctor, Ruiz Lorenzo, J. J.
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/45061
Acceso en línea:https://hdl.handle.net/20.500.14352/45061
Access Level:acceso abierto
Palabra clave:53
51-73
Antiferromagnetic RP(2) model
Monte-Carlo simulations
State Potts-model
3 dimensions
milticritical point
Critical exponents
Ising-model
Renormalization
Temperature
Ensemble
Física (Física)
Física-Modelos matemáticos
22 Física
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oai_identifier_str oai:docta.ucm.es:20.500.14352/45061
network_acronym_str ES
network_name_str España
repository_id_str
spelling Microcanonical finite-size scaling in second-order phase transitions with diverging specific heatFernández Pérez, Luis AntonioGordillo Guerrero, A.Martín Mayor, VíctorRuiz Lorenzo, J. J.5351-73Antiferromagnetic RP(2) modelMonte-Carlo simulationsState Potts-model3 dimensionsmilticritical pointCritical exponentsIsing-modelRenormalizationTemperatureEnsembleFísica (Física)Física-Modelos matemáticos22 FísicaA microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.American Physical SocietyUniversidad Complutense de Madrid20092009-11-0620092009-11-06journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/45061reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/450612026-06-02T12:44:21Z
dc.title.none.fl_str_mv Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
title Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
spellingShingle Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
Fernández Pérez, Luis Antonio
53
51-73
Antiferromagnetic RP(2) model
Monte-Carlo simulations
State Potts-model
3 dimensions
milticritical point
Critical exponents
Ising-model
Renormalization
Temperature
Ensemble
Física (Física)
Física-Modelos matemáticos
22 Física
title_short Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
title_full Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
title_fullStr Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
title_full_unstemmed Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
title_sort Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
dc.creator.none.fl_str_mv Fernández Pérez, Luis Antonio
Gordillo Guerrero, A.
Martín Mayor, Víctor
Ruiz Lorenzo, J. J.
author Fernández Pérez, Luis Antonio
author_facet Fernández Pérez, Luis Antonio
Gordillo Guerrero, A.
Martín Mayor, Víctor
Ruiz Lorenzo, J. J.
author_role author
author2 Gordillo Guerrero, A.
Martín Mayor, Víctor
Ruiz Lorenzo, J. J.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 53
51-73
Antiferromagnetic RP(2) model
Monte-Carlo simulations
State Potts-model
3 dimensions
milticritical point
Critical exponents
Ising-model
Renormalization
Temperature
Ensemble
Física (Física)
Física-Modelos matemáticos
22 Física
topic 53
51-73
Antiferromagnetic RP(2) model
Monte-Carlo simulations
State Potts-model
3 dimensions
milticritical point
Critical exponents
Ising-model
Renormalization
Temperature
Ensemble
Física (Física)
Física-Modelos matemáticos
22 Física
description A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-11-06
2009
2009-11-06
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/45061
url https://hdl.handle.net/20.500.14352/45061
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869420017821417472
score 15.301603

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