Gibbs–non-Gibbs properties for evolving Ising models on trees
| Autor: | Victor Ermolaev, Aernout C.D. van Enter, Christof Külske, Giulio Iacobelli |
|---|---|
| Přispěvatelé: | Stochastic Studies and Statistics |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Statistics and Probability
82C20 82B20 BETHE LATTICE TRANSITIONS Gibbs state Glauber dynamics Combinatorics Ising models Mathematics::Probability Tree graphs Intermediate state Statistical physics Mathematics GIBBSIANNESS Bethe lattice Zero (complex analysis) State (functional analysis) RECOVERY QUASILOCALITY Nonlinear Sciences::Cellular Automata and Lattice Gases Tree (graph theory) STATE 60K35 Cayley tree Condensed Matter::Statistical Mechanics Mathematics::Mathematical Physics Ising model Statistics Probability and Uncertainty Non-Gibbsianness Glauber |
| Zdroj: | Annales de l institut henri poincare-Probabilites et statistiques, 48(3), 774-791 Ann. Inst. H. Poincaré Probab. Statist. 48, no. 3 (2012), 774-791 |
| ISSN: | 0246-0203 |
| Popis: | In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the free-boundary-condition Gibbs state) behaves differently from the plus and the minus state. E.g. at large times, all configurations are bad for the intermediate state, whereas the plus configuration never is bad for the plus state. Moreover, we show that for each state there are two transitions. For the intermediate state there is a transition from a Gibbsian regime to a non-Gibbsian regime where some, but not all configurations are bad, and a second one to a regime where all configurations are bad. ¶ For the plus and minus state, the two transitions are from a Gibbsian regime to a non-Gibbsian one and then back to a Gibbsian regime again. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|