Tsallis scaling in the long-range Ising chain with competitive interactions
Autor(a) principal: | |
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Data de Publicação: | 2009 |
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=S0103-97332009000400012 |
Resumo: | A numerically efficient transfer matrix approach is used to investigate the validity of the Tsallis scaling hypothesis in the long-range Ising spin chain with competitive interactions. In this model, the interaction between two spins i and j placed r lattice steps apart is Ji, j = (-1)ζ(i,j)J0/rα, where ζ(i, j) is either 0 or 1. This procedure has succeeded to show the validity of the scaling hypothesis for the well investigated ferromagnetic version of the model, i.e., ζ(i, j)= 0,∀i, j, ∀α > 0. Results are reported for some models of a set, which is defined by requiring ζ(i, j) to be a periodic sequence of 0's and 1's. As expected from symmetry arguments, we find that the hypothesis is not valid when ζ(i, j)= 1,∀i, j and α < 1. however, it is verified, with high degree of numerical accuracy, when α < 1, for sequences in which the occurrence of ζ(i, j)= 0 is more frequent than that of ζ(i, j)= 1. |
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Brazilian Journal of Physics |
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spelling |
Tsallis scaling in the long-range Ising chain with competitive interactionsCompetitive interactionsLong-range Ising chainA numerically efficient transfer matrix approach is used to investigate the validity of the Tsallis scaling hypothesis in the long-range Ising spin chain with competitive interactions. In this model, the interaction between two spins i and j placed r lattice steps apart is Ji, j = (-1)ζ(i,j)J0/rα, where ζ(i, j) is either 0 or 1. This procedure has succeeded to show the validity of the scaling hypothesis for the well investigated ferromagnetic version of the model, i.e., ζ(i, j)= 0,∀i, j, ∀α > 0. Results are reported for some models of a set, which is defined by requiring ζ(i, j) to be a periodic sequence of 0's and 1's. As expected from symmetry arguments, we find that the hypothesis is not valid when ζ(i, j)= 1,∀i, j and α < 1. however, it is verified, with high degree of numerical accuracy, when α < 1, for sequences in which the occurrence of ζ(i, j)= 0 is more frequent than that of ζ(i, j)= 1.Sociedade Brasileira de Física2009-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332009000400012Brazilian Journal of Physics v.39 n.2a 2009reponame:Brazilian Journal of Physicsinstname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S0103-97332009000400012info:eu-repo/semantics/openAccessCarvalho Neto,E. M.Andrade,R. F. S.eng2009-09-10T00:00:00Zoai:scielo:S0103-97332009000400012Revistahttp://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:2009-09-10T00:00Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
Tsallis scaling in the long-range Ising chain with competitive interactions |
title |
Tsallis scaling in the long-range Ising chain with competitive interactions |
spellingShingle |
Tsallis scaling in the long-range Ising chain with competitive interactions Carvalho Neto,E. M. Competitive interactions Long-range Ising chain |
title_short |
Tsallis scaling in the long-range Ising chain with competitive interactions |
title_full |
Tsallis scaling in the long-range Ising chain with competitive interactions |
title_fullStr |
Tsallis scaling in the long-range Ising chain with competitive interactions |
title_full_unstemmed |
Tsallis scaling in the long-range Ising chain with competitive interactions |
title_sort |
Tsallis scaling in the long-range Ising chain with competitive interactions |
author |
Carvalho Neto,E. M. |
author_facet |
Carvalho Neto,E. M. Andrade,R. F. S. |
author_role |
author |
author2 |
Andrade,R. F. S. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Carvalho Neto,E. M. Andrade,R. F. S. |
dc.subject.por.fl_str_mv |
Competitive interactions Long-range Ising chain |
topic |
Competitive interactions Long-range Ising chain |
description |
A numerically efficient transfer matrix approach is used to investigate the validity of the Tsallis scaling hypothesis in the long-range Ising spin chain with competitive interactions. In this model, the interaction between two spins i and j placed r lattice steps apart is Ji, j = (-1)ζ(i,j)J0/rα, where ζ(i, j) is either 0 or 1. This procedure has succeeded to show the validity of the scaling hypothesis for the well investigated ferromagnetic version of the model, i.e., ζ(i, j)= 0,∀i, j, ∀α > 0. Results are reported for some models of a set, which is defined by requiring ζ(i, j) to be a periodic sequence of 0's and 1's. As expected from symmetry arguments, we find that the hypothesis is not valid when ζ(i, j)= 1,∀i, j and α < 1. however, it is verified, with high degree of numerical accuracy, when α < 1, for sequences in which the occurrence of ζ(i, j)= 0 is more frequent than that of ζ(i, j)= 1. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-08-01 |
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=S0103-97332009000400012 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332009000400012 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0103-97332009000400012 |
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.39 n.2a 2009 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_ |
1754734865168728064 |