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Article: Generalized Frenkel-Kontorova models

TitleGeneralized Frenkel-Kontorova models
Authors
Issue Date1994
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/physa
Citation
Physica A: Statistical Mechanics and its Applications, 1994, v. 205 n. 1-3, p. 420-442 How to Cite?
AbstractWe have studied two generalized Frenkel-Kontorova (FK) models. In one of them the interatomic potential is changed from simple harmonic to Toda; in the other the external potential is changed from sinusoidal to nonanalytic. Their critical behaviors are found to be markedly different. In the Toda case, the local critical exponents are the same as those in the standard FK model. However, the global singularity spectrum and the generalized dimension depend on the anharmonicity parameter. In the nonanalytic FK model, the critical exponents are found to vary with the degree of inflection z for 2≤z<3, but remain the same for z≥3. The degree of inflection thus plays a role quite similar to that of dimensionality in phase transitions with z = 2 and 3 corresponding respectively to the lower and upper critical dimensions. For z>3, a sequence of pinning and depinning transitions, reflecting the recurrence of Kolmogorov-Arnol'd-Moser tori, has also been observed. © 1994.
Persistent Identifierhttp://hdl.handle.net/10722/90805
ISSN
2015 Impact Factor: 1.785
2015 SCImago Journal Rankings: 0.738

 

DC FieldValueLanguage
dc.contributor.authorHu, Ben_HK
dc.contributor.authorLin, Ben_HK
dc.contributor.authorShi, Jen_HK
dc.date.accessioned2010-09-17T10:08:39Z-
dc.date.available2010-09-17T10:08:39Z-
dc.date.issued1994en_HK
dc.identifier.citationPhysica A: Statistical Mechanics and its Applications, 1994, v. 205 n. 1-3, p. 420-442en_HK
dc.identifier.issn0378-4371en_HK
dc.identifier.urihttp://hdl.handle.net/10722/90805-
dc.description.abstractWe have studied two generalized Frenkel-Kontorova (FK) models. In one of them the interatomic potential is changed from simple harmonic to Toda; in the other the external potential is changed from sinusoidal to nonanalytic. Their critical behaviors are found to be markedly different. In the Toda case, the local critical exponents are the same as those in the standard FK model. However, the global singularity spectrum and the generalized dimension depend on the anharmonicity parameter. In the nonanalytic FK model, the critical exponents are found to vary with the degree of inflection z for 2≤z<3, but remain the same for z≥3. The degree of inflection thus plays a role quite similar to that of dimensionality in phase transitions with z = 2 and 3 corresponding respectively to the lower and upper critical dimensions. For z>3, a sequence of pinning and depinning transitions, reflecting the recurrence of Kolmogorov-Arnol'd-Moser tori, has also been observed. © 1994.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/physaen_HK
dc.relation.ispartofPhysica A: Statistical Mechanics and its Applicationsen_HK
dc.titleGeneralized Frenkel-Kontorova modelsen_HK
dc.typeArticleen_HK
dc.identifier.emailLin, B:blin@hku.hken_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-0013136515en_HK
dc.identifier.volume205en_HK
dc.identifier.issue1-3en_HK
dc.identifier.spage420en_HK
dc.identifier.epage442en_HK

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