Sensitive Dependence of Gibbs Measures at Low Temperatures

Daniel Coronel, Juan Rivera-Letelier

Resultado de la investigación: Article

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

Huella dactilar

Gibbs Measure
Interaction
Lattice System
interactions
perturbation
Lipschitz
Perturbation
Configuration Space
Small Perturbations
Smooth function
Nearest Neighbor
State Space
topology
Topology
Decrease
Zero
configurations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Citar esto

Coronel, Daniel ; Rivera-Letelier, Juan. / Sensitive Dependence of Gibbs Measures at Low Temperatures. En: Journal of Statistical Physics. 2015 ; Vol. 160, N.º 6. pp. 1658-1683.
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Sensitive Dependence of Gibbs Measures at Low Temperatures. / Coronel, Daniel; Rivera-Letelier, Juan.

En: Journal of Statistical Physics, Vol. 160, N.º 6, 14.09.2015, p. 1658-1683.

Resultado de la investigación: Article

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