Zero-temperature phase diagram for double-well type potentials in the summable variation class
| Autor: | Philippe Thieullen, Rodrigo Bissacot, Eduardo Garibaldi |
|---|---|
| Přispěvatelé: | Institute of Mathematics and Statistics [Sao Paulo] (IME-USP), Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC), Universidade Estadual de Campinas (UNICAMP), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2016 |
| Předmět: |
Applied Mathematics
General Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 010102 general mathematics Zero (complex analysis) Dynamical Systems (math.DS) Fixed point Type (model theory) Space (mathematics) Lipschitz continuity 01 natural sciences 010305 fluids & plasmas [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Transfer operator 37D35 37A60 37B10 82Bxx 0103 physical sciences FOS: Mathematics SISTEMAS DINÂMICOS Mathematics - Dynamical Systems 0101 mathematics Constant (mathematics) Phase diagram Mathematical physics Mathematics |
| Zdroj: | Ergodic Theory and Dynamical Systems Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2018, 38 (3) Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/etds.2016.57 |
| Popis: | We study the zero-temperature limit of the Gibbs measures of a class of long-range potentials on a full shift of two symbols $\{0,1\}$. These potentials were introduced by Walters as a natural space for the transfer operator. In our case, they are locally constant, Lipschitz continuous or, more generally, of summable variation. We assume there exists exactly two ground states: the fixed points $0^\infty$ and $1^\infty$. We fully characterize, in terms of the Peierls barrier between the two ground states, the zero-temperature phase diagram of such potentials, that is, the regions of convergence or divergence of the Gibbs measures as the temperature goes to zero. 27 pages, 2 figures. To appear in Ergodic Theory and Dynamical Systems |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|