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General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Interdisciplinar de Sistemas Complejos (GISC)es
dc.contributor.authorCuesta, José A.
dc.contributor.authorSánchez, Angel
dc.date.accessioned2012-07-20T10:27:26Z
dc.date.available2012-07-20T10:27:26Z
dc.date.issued2004-05
dc.description.abstractWe examine critically the issue of phase transitions in one-dimensional systems with short range interactions. We begin by reviewing in detail the most famous non-existence result, namely van Hove’s theorem, emphasizing its hypothesis and subsequently its limited range of applicability. To further underscore this point, we present several examples of one-dimensional short ranged models that exhibit true, thermodynamic phase transitions, with increasing level of complexity and closeness to reality. Thus having made clear the necessity for a result broader than van Hove’s theorem, we set out to prove such a general non-existence theorem, widening largely the class of models known to be free of phase transitions. The theorem is presented from a rigorous mathematical point of view although examples of the framework corresponding to usual physical systems are given along the way. We close the paper with a discussion in more physical terms of the implications of this non-existence theorem
dc.description.sponsorshipThis work has been supported by the Ministerio de Ciencia y Tecnología of Spain through Grants BFM2000-0004 (JAC) and BFM2000-0006 (AS).
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Statistical Physics, vol. 115, n. 3-4, mayo 2004. Pp. 869-893
dc.identifier.doi10.1023/B:JOSS.0000022373.63640.4e
dc.identifier.issn0022-4715 (print version)
dc.identifier.issn1572-9613 (electronic version)
dc.identifier.publicationfirstpage869
dc.identifier.publicationissuen. 3-4
dc.identifier.publicationlastpage893
dc.identifier.publicationtitleJournal of Statistical Physics
dc.identifier.publicationvolumevol. 115
dc.identifier.urihttps://hdl.handle.net/10016/14953
dc.language.isoeng
dc.publisherSpringer
dc.relation.publisherversionhttp://dx.doi.org/10.1023/B:JOSS.0000022373.63640.4e
dc.rights© Springer
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherPhase transitions
dc.subject.otherOne-dimensional systems
dc.subject.otherShort-range interactions
dc.subject.otherTransfer operators
dc.subject.otherRigorous results
dc.titleGeneral non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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