### 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 original | Inglés |
---|---|

Páginas (desde-hasta) | 1658-1683 |

Número de páginas | 26 |

Publicación | Journal of Statistical Physics |

Volumen | 160 |

N.º | 6 |

DOI | |

Estado | Publicada - 14 sep 2015 |

### Áreas temáticas de ASJC Scopus

- Física estadística y no lineal
- Física matemática

## Huella Profundice en los temas de investigación de 'Sensitive Dependence of Gibbs Measures at Low Temperatures'. En conjunto forman una huella única.

## Citar esto

*Journal of Statistical Physics*,

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