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Abstract:

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.

Registro:

Documento: Artículo
Título:Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction
Autor:Fernández, R.; den Hollander, F.; Martínez, J.
Filiación:Department of Mathematics, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, Netherlands
Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, Netherlands
Instituto de Investigaciones Matemáticas Luis A. Santaló, Conicet, C1428EGA Buenos Aires, Argentina
Palabras clave:Action integral; Bifurcation of rate function; Curie-Weiss model; Dynamical transition; Gibbs versus non-Gibbs; Kac model; Large deviation principles; Spin-flip dynamics
Año:2014
Volumen:156
Número:2
Página de inicio:203
Página de fin:220
DOI: http://dx.doi.org/10.1007/s10955-014-1004-0
Título revista:Journal of Statistical Physics
Título revista abreviado:J. Stat. Phys.
ISSN:00224715
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v156_n2_p203_Fernandez

Referencias:

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Citas:

---------- APA ----------
Fernández, R., den Hollander, F. & Martínez, J. (2014) . Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction. Journal of Statistical Physics, 156(2), 203-220.
http://dx.doi.org/10.1007/s10955-014-1004-0
---------- CHICAGO ----------
Fernández, R., den Hollander, F., Martínez, J. "Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction" . Journal of Statistical Physics 156, no. 2 (2014) : 203-220.
http://dx.doi.org/10.1007/s10955-014-1004-0
---------- MLA ----------
Fernández, R., den Hollander, F., Martínez, J. "Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction" . Journal of Statistical Physics, vol. 156, no. 2, 2014, pp. 203-220.
http://dx.doi.org/10.1007/s10955-014-1004-0
---------- VANCOUVER ----------
Fernández, R., den Hollander, F., Martínez, J. Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction. J. Stat. Phys. 2014;156(2):203-220.
http://dx.doi.org/10.1007/s10955-014-1004-0