Critical behavior of ferromagnetic spin models with aperiodic exchange interactions

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dc.creatorHaddad, T. A. S.
dc.creatorPinho, S. T. R.
dc.creatorSalinas, S. R.
dc.date2000-09-08
dc.date2000-09-11
dc.date.accessioned2026-07-07T02:38:40Z
dc.date.available2026-07-07T02:38:40Z
dc.descriptionWe review recent investigations of the critical behavior of ferromagnetic $q$-state Potts models on a class of hierarchical lattices, with exchange interactions according to some deterministic but aperiodic substitution rules. The problem is formulated in terms of exact recursion relations on a suitable parameter space. The analysis of the fixed points of these equations leads to a criterion to gauge the relevance of the aperiodic geometric fluctuations. For irrelevant fluctuations, the critical behavior remains unchanged with respect to the underlying uniform models. In the presence of relevant fluctuations, a non-trivial symmetric fixed point, associated with the critical behavior of the uniform model, becomes fully unstable, and there appears a two-cycle of the recursion relations. A scaling analysis, supported by direct numerical thermodynamical calculations, shows the existence of a novel critical universality class associated with relevant geometric fluctuations.
dc.description8 pages, 2 ps figures (included). Presented at the "Ising Centennial Colloquium", Belo Horizonte, Brazil, Aug. 1-4, 2000. To appear in the Brazilian Journal of Physics (available at http://www.sbf.if.usp.br/bjp). References corrected and updated
dc.identifierhttps://arxiv.org/abs/cond-mat/0009135
dc.identifierhttp://arxiv.org/abs/cond-mat/0009135
dc.identifierBraz. J. Phys. 30, 741 (2000)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/16757
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleCritical behavior of ferromagnetic spin models with aperiodic exchange interactions
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