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...

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Detalles Bibliográficos
Publicado: 2014
Materias:
Action integral
Bifurcation of rate function
Curie-Weiss model
Dynamical transition
Gibbs versus non-Gibbs
Kac model
Large deviation principles
Spin-flip dynamics
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v156_n2_p203_Fernandez
http://hdl.handle.net/20.500.12110/paper_00224715_v156_n2_p203_Fernandez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00224715_v156_n2_p203_Fernandez
record_format dspace
spelling paper:paper_00224715_v156_n2_p203_Fernandez2023-06-08T14:50:55Z Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v156_n2_p203_Fernandez 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
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.
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
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v156_n2_p203_Fernandez
http://hdl.handle.net/20.500.12110/paper_00224715_v156_n2_p203_Fernandez
_version_ 1768541692999237632

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