Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction
We continue our study of Gibbs-non-Gibbs dynamical transitions. In the present paper we consider a system of Ising spins on a large discrete torus with a Kac-type interaction subject to an independent spin-flip dynamics (infinite-temperature Glauber dynamics). We show that, in accordance with the pr...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00224715_v156_n2_p203_Fernandez |
| Aporte de: |
| id |
todo:paper_00224715_v156_n2_p203_Fernandez |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00224715_v156_n2_p203_Fernandez2023-10-03T14:32:57Z Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction Fernández, R. den Hollander, F. Martínez, J. Action integral Bifurcation of rate function Curie-Weiss model Dynamical transition Gibbs versus non-Gibbs Kac model Large deviation principles Spin-flip dynamics We continue our study of Gibbs-non-Gibbs dynamical transitions. In the present paper we consider a system of Ising spins on a large discrete torus with a Kac-type interaction subject to an independent spin-flip dynamics (infinite-temperature Glauber dynamics). We show that, in accordance with the program outlined in van Enter et al. (Moscow Math. J. 10:687-711, 2010), in the thermodynamic limit Gibbs-non-Gibbs dynamical transitions are equivalent to bifurcations in the set of global minima of the large-deviation rate function for the trajectories of the empirical density conditional on their endpoint. More precisely, the time-evolved measure is non-Gibbs if and only if this set is not a singleton for some value of the endpoint. A partial description of the possible scenarios of bifurcation is given, leading to a characterization of passages from Gibbs to non-Gibbs and vice versa, with sharp transition times. Our analysis provides a conceptual step-up from our earlier work on Gibbs-non-Gibbs dynamical transitions for the Curie-Weiss model, where the mean-field interaction allowed us to focus on trajectories of the empirical magnetization rather than the empirical density. © 2014 Springer Science+Business Media New York. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00224715_v156_n2_p203_Fernandez |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Action integral Bifurcation of rate function Curie-Weiss model Dynamical transition Gibbs versus non-Gibbs Kac model Large deviation principles Spin-flip dynamics |
| spellingShingle |
Action integral Bifurcation of rate function Curie-Weiss model Dynamical transition Gibbs versus non-Gibbs Kac model Large deviation principles Spin-flip dynamics Fernández, R. den Hollander, F. Martínez, J. Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction |
| topic_facet |
Action integral Bifurcation of rate function Curie-Weiss model Dynamical transition Gibbs versus non-Gibbs Kac model Large deviation principles Spin-flip dynamics |
| description |
We continue our study of Gibbs-non-Gibbs dynamical transitions. In the present paper we consider a system of Ising spins on a large discrete torus with a Kac-type interaction subject to an independent spin-flip dynamics (infinite-temperature Glauber dynamics). We show that, in accordance with the program outlined in van Enter et al. (Moscow Math. J. 10:687-711, 2010), in the thermodynamic limit Gibbs-non-Gibbs dynamical transitions are equivalent to bifurcations in the set of global minima of the large-deviation rate function for the trajectories of the empirical density conditional on their endpoint. More precisely, the time-evolved measure is non-Gibbs if and only if this set is not a singleton for some value of the endpoint. A partial description of the possible scenarios of bifurcation is given, leading to a characterization of passages from Gibbs to non-Gibbs and vice versa, with sharp transition times. Our analysis provides a conceptual step-up from our earlier work on Gibbs-non-Gibbs dynamical transitions for the Curie-Weiss model, where the mean-field interaction allowed us to focus on trajectories of the empirical magnetization rather than the empirical density. © 2014 Springer Science+Business Media New York. |
| format |
JOUR |
| author |
Fernández, R. den Hollander, F. Martínez, J. |
| author_facet |
Fernández, R. den Hollander, F. Martínez, J. |
| author_sort |
Fernández, R. |
| title |
Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction |
| title_short |
Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction |
| title_full |
Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction |
| title_fullStr |
Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction |
| title_full_unstemmed |
Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction |
| title_sort |
variational description of gibbs-non-gibbs dynamical transitions for spin-flip systems with a kac-type interaction |
| url |
http://hdl.handle.net/20.500.12110/paper_00224715_v156_n2_p203_Fernandez |
| work_keys_str_mv |
AT fernandezr variationaldescriptionofgibbsnongibbsdynamicaltransitionsforspinflipsystemswithakactypeinteraction AT denhollanderf variationaldescriptionofgibbsnongibbsdynamicaltransitionsforspinflipsystemswithakactypeinteraction AT martinezj variationaldescriptionofgibbsnongibbsdynamicaltransitionsforspinflipsystemswithakactypeinteraction |
| _version_ |
1807318455798464512 |