Sensitive Dependence of Gibbs Measures at Low Temperatures

Daniel Coronel, Juan Rivera-Letelier

Research output: Contribution to journalArticlepeer-review

11 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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