Sensitive Dependence of Gibbs Measures at Low Temperatures

Daniel Coronel, Juan Rivera-Letelier

Resultado de la investigación: Contribución a una revistaArtículo

8 Citas (Scopus)

Resumen

The Gibbs measures of an interaction can behave chaotically as the temperature drops to zero. We observe that for some classical lattice systems there are interactions exhibiting a related phenomenon of sensitive dependence of Gibbs measures: An arbitrarily small perturbation of the interaction can produce significant changes in the low-temperature behavior of its Gibbs measures. For some one-dimensional XY models we exhibit sensitive dependence of Gibbs measures for a (nearest-neighbor) interaction given by a smooth function, and for perturbations that are small in the smooth category. We also exhibit sensitive dependence of Gibbs measures for an interaction on a classical lattice system with finite-state space. This interaction decreases exponentially as a function of the distance between sites; it is given by a Lipschitz continuous potential in the configuration space. The perturbations are small in the Lipschitz topology. As a by-product we solve some problems stated by Chazottes and Hochman.

Idioma originalInglés
Páginas (desde-hasta)1658-1683
Número de páginas26
PublicaciónJournal of Statistical Physics
Volumen160
N.º6
DOI
EstadoPublicada - 14 sep 2015

Áreas temáticas de ASJC Scopus

  • Física estadística y no lineal
  • Física matemática

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