Bond counting Monte Carlo for the 2-D Ising model in an external field
Autor(a) principal: | |
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Data de Publicação: | 2000 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Brazilian Journal of Physics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332000000400013 |
Resumo: | We propose an improvement of a Monte Carlo method designed to treat the Ising model in a field [C. Lieu and J. Florencio, J. Low Temp. Phys. 89, 565 (1992)]. The method involves the counting of bonds linking neighboring like-spins and yields the degeneracy of the system's energy states, hence the partition function. There is no acceptance-rejection procedure and all the randomly generated configurations are kept. The sampling depends on geometry only, so results of a given run can be used for all temperatures and energy parameters. In order to understand the virtues and inadequacies of the method, we obtained exact results for small lattices. We find that a Monte Carlo run must be followed by a Gaussian fit in order to account properly for the rare events not recorded in the sampling. Finally, we also established bounds for the location of the peak for the specifc heat of the Ising model in a magnetic field in two dimensions for several values of the field in the thermodynamic limit. |
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Brazilian Journal of Physics |
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Bond counting Monte Carlo for the 2-D Ising model in an external fieldWe propose an improvement of a Monte Carlo method designed to treat the Ising model in a field [C. Lieu and J. Florencio, J. Low Temp. Phys. 89, 565 (1992)]. The method involves the counting of bonds linking neighboring like-spins and yields the degeneracy of the system's energy states, hence the partition function. There is no acceptance-rejection procedure and all the randomly generated configurations are kept. The sampling depends on geometry only, so results of a given run can be used for all temperatures and energy parameters. In order to understand the virtues and inadequacies of the method, we obtained exact results for small lattices. We find that a Monte Carlo run must be followed by a Gaussian fit in order to account properly for the rare events not recorded in the sampling. Finally, we also established bounds for the location of the peak for the specifc heat of the Ising model in a magnetic field in two dimensions for several values of the field in the thermodynamic limit.Sociedade Brasileira de Física2000-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332000000400013Brazilian Journal of Physics v.30 n.4 2000reponame:Brazilian Journal of Physicsinstname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S0103-97332000000400013info:eu-repo/semantics/openAccessDias,H. G.Florencio,J.eng2002-01-09T00:00:00Zoai:scielo:S0103-97332000000400013Revistahttp://www.sbfisica.org.br/v1/home/index.php/pt/ONGhttps://old.scielo.br/oai/scielo-oai.phpsbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br1678-44480103-9733opendoar:2002-01-09T00:00Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
Bond counting Monte Carlo for the 2-D Ising model in an external field |
title |
Bond counting Monte Carlo for the 2-D Ising model in an external field |
spellingShingle |
Bond counting Monte Carlo for the 2-D Ising model in an external field Dias,H. G. |
title_short |
Bond counting Monte Carlo for the 2-D Ising model in an external field |
title_full |
Bond counting Monte Carlo for the 2-D Ising model in an external field |
title_fullStr |
Bond counting Monte Carlo for the 2-D Ising model in an external field |
title_full_unstemmed |
Bond counting Monte Carlo for the 2-D Ising model in an external field |
title_sort |
Bond counting Monte Carlo for the 2-D Ising model in an external field |
author |
Dias,H. G. |
author_facet |
Dias,H. G. Florencio,J. |
author_role |
author |
author2 |
Florencio,J. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Dias,H. G. Florencio,J. |
description |
We propose an improvement of a Monte Carlo method designed to treat the Ising model in a field [C. Lieu and J. Florencio, J. Low Temp. Phys. 89, 565 (1992)]. The method involves the counting of bonds linking neighboring like-spins and yields the degeneracy of the system's energy states, hence the partition function. There is no acceptance-rejection procedure and all the randomly generated configurations are kept. The sampling depends on geometry only, so results of a given run can be used for all temperatures and energy parameters. In order to understand the virtues and inadequacies of the method, we obtained exact results for small lattices. We find that a Monte Carlo run must be followed by a Gaussian fit in order to account properly for the rare events not recorded in the sampling. Finally, we also established bounds for the location of the peak for the specifc heat of the Ising model in a magnetic field in two dimensions for several values of the field in the thermodynamic limit. |
publishDate |
2000 |
dc.date.none.fl_str_mv |
2000-12-01 |
dc.type.driver.fl_str_mv |
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://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332000000400013 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332000000400013 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0103-97332000000400013 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
dc.source.none.fl_str_mv |
Brazilian Journal of Physics v.30 n.4 2000 reponame:Brazilian Journal of Physics instname:Sociedade Brasileira de Física (SBF) instacron:SBF |
instname_str |
Sociedade Brasileira de Física (SBF) |
instacron_str |
SBF |
institution |
SBF |
reponame_str |
Brazilian Journal of Physics |
collection |
Brazilian Journal of Physics |
repository.name.fl_str_mv |
Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF) |
repository.mail.fl_str_mv |
sbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br |
_version_ |
1754734859144658944 |