### 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 language | English |
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Pages (from-to) | 1658-1683 |

Number of pages | 26 |

Journal | Journal of Statistical Physics |

Volume | 160 |

Issue number | 6 |

DOIs | |

Publication status | Published - 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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## Cite this

*Journal of Statistical Physics*,

*160*(6), 1658-1683. https://doi.org/10.1007/s10955-015-1288-8