Sensitive Dependence of Gibbs Measures at Low Temperatures
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Fecha
2015-09
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Facultad/escuela
Idioma
en
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Editor
Springer New York LLC
Nombre de Curso
Licencia CC
Atribución 4.0 Internacional (CC BY 4.0)
Licencia CC
https://creativecommons.org/licenses/by/4.0/deed.es
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. © 2015, Springer Science+Business Media New York.
Notas
Indexación: Scopus
Palabras clave
Hamiltonian, Stochastic Homogenization, Arnold Diffusion
Citación
DOI
10.1007/s10955-015-1288-8