Solution on the bethe lattice of a hard core athermal gas with two kinds of particles
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | LOCUS Repositório Institucional da UFV |
Texto Completo: | https://doi.org/10.1063/1.3658045 http://www.locus.ufv.br/handle/123456789/19316 |
Resumo: | Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here, we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which, when placed on a site, do not allow other particles to occupy its first neighbors also. We solve the model on a Bethe lattice of arbitrary coordination number q. In the parameter space defined by the activities of both particles, at low values of the activity of small particles (z1) we find a continuous transition from the fluid to the solid phase as the activity of large particles (z2) is increased. At higher values of z1 the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at z1 = 0 and displays a minimum before reaching the tricritical point, so that a re-entrant behavior is observed for constant values of z2 in the region of low density of small particles. The isobaric curves of the total density of particles as a function of the density or the activity of small particles show a minimum in the fluid phase. |
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Oliveira, Tiago J.Stilck, Jürgen F.2018-05-03T18:08:31Z2018-05-03T18:08:31Z2011-10-141089-7690https://doi.org/10.1063/1.3658045http://www.locus.ufv.br/handle/123456789/19316Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here, we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which, when placed on a site, do not allow other particles to occupy its first neighbors also. We solve the model on a Bethe lattice of arbitrary coordination number q. In the parameter space defined by the activities of both particles, at low values of the activity of small particles (z1) we find a continuous transition from the fluid to the solid phase as the activity of large particles (z2) is increased. At higher values of z1 the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at z1 = 0 and displays a minimum before reaching the tricritical point, so that a re-entrant behavior is observed for constant values of z2 in the region of low density of small particles. The isobaric curves of the total density of particles as a function of the density or the activity of small particles show a minimum in the fluid phase.engThe Journal of Chemical Physicsv. 135, p. 1845021-1845027, nov. 2011American Institute of Physicsinfo:eu-repo/semantics/openAccessSolutionBethe latticeHard core athermal gas with two kinds of particlesSolution on the bethe lattice of a hard core athermal gas with two kinds of particlesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfreponame:LOCUS Repositório Institucional da UFVinstname:Universidade Federal de Viçosa (UFV)instacron:UFVORIGINALartigo.pdfartigo.pdftexto completoapplication/pdf617378https://locus.ufv.br//bitstream/123456789/19316/1/artigo.pdff6b5468888f9b836b4979c94d00a5880MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/19316/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILartigo.pdf.jpgartigo.pdf.jpgIM Thumbnailimage/jpeg4250https://locus.ufv.br//bitstream/123456789/19316/3/artigo.pdf.jpg5a1dba059d21945bb78abb1563b408ccMD53123456789/193162018-05-03 23:00:39.045oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-05-04T02:00:39LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false |
dc.title.en.fl_str_mv |
Solution on the bethe lattice of a hard core athermal gas with two kinds of particles |
title |
Solution on the bethe lattice of a hard core athermal gas with two kinds of particles |
spellingShingle |
Solution on the bethe lattice of a hard core athermal gas with two kinds of particles Oliveira, Tiago J. Solution Bethe lattice Hard core athermal gas with two kinds of particles |
title_short |
Solution on the bethe lattice of a hard core athermal gas with two kinds of particles |
title_full |
Solution on the bethe lattice of a hard core athermal gas with two kinds of particles |
title_fullStr |
Solution on the bethe lattice of a hard core athermal gas with two kinds of particles |
title_full_unstemmed |
Solution on the bethe lattice of a hard core athermal gas with two kinds of particles |
title_sort |
Solution on the bethe lattice of a hard core athermal gas with two kinds of particles |
author |
Oliveira, Tiago J. |
author_facet |
Oliveira, Tiago J. Stilck, Jürgen F. |
author_role |
author |
author2 |
Stilck, Jürgen F. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Oliveira, Tiago J. Stilck, Jürgen F. |
dc.subject.pt-BR.fl_str_mv |
Solution Bethe lattice Hard core athermal gas with two kinds of particles |
topic |
Solution Bethe lattice Hard core athermal gas with two kinds of particles |
description |
Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here, we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which, when placed on a site, do not allow other particles to occupy its first neighbors also. We solve the model on a Bethe lattice of arbitrary coordination number q. In the parameter space defined by the activities of both particles, at low values of the activity of small particles (z1) we find a continuous transition from the fluid to the solid phase as the activity of large particles (z2) is increased. At higher values of z1 the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at z1 = 0 and displays a minimum before reaching the tricritical point, so that a re-entrant behavior is observed for constant values of z2 in the region of low density of small particles. The isobaric curves of the total density of particles as a function of the density or the activity of small particles show a minimum in the fluid phase. |
publishDate |
2011 |
dc.date.issued.fl_str_mv |
2011-10-14 |
dc.date.accessioned.fl_str_mv |
2018-05-03T18:08:31Z |
dc.date.available.fl_str_mv |
2018-05-03T18:08:31Z |
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 |
https://doi.org/10.1063/1.3658045 http://www.locus.ufv.br/handle/123456789/19316 |
dc.identifier.issn.none.fl_str_mv |
1089-7690 |
identifier_str_mv |
1089-7690 |
url |
https://doi.org/10.1063/1.3658045 http://www.locus.ufv.br/handle/123456789/19316 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartofseries.pt-BR.fl_str_mv |
v. 135, p. 1845021-1845027, nov. 2011 |
dc.rights.driver.fl_str_mv |
American Institute of Physics info:eu-repo/semantics/openAccess |
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American Institute of Physics |
eu_rights_str_mv |
openAccess |
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application/pdf |
dc.publisher.none.fl_str_mv |
The Journal of Chemical Physics |
publisher.none.fl_str_mv |
The Journal of Chemical Physics |
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LOCUS Repositório Institucional da UFV |
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