Sensitive Dependence of Gibbs Measures at Low Temperatures

Daniel Coronel, Juan Rivera-Letelier

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1658-1683
Number of pages26
JournalJournal of Statistical Physics
Volume160
Issue number6
DOIs
Publication statusPublished - 14 Sep 2015

Keywords

  • Lattice system
  • Low-temperature Gibbs measure
  • XY models

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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