Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction

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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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Autor principal: Fernández, R.
Otros Autores: den Hollander, F., Martínez, J.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Springer New York LLC 2014
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100 1 |a Fernández, R. 
245 1 0 |a Variational Description of Gibbs-Non-Gibbs Dynamical Transitions for Spin-Flip Systems with a Kac-Type Interaction 
260 |b Springer New York LLC  |c 2014 
270 1 0 |m Fernández, R.; Department of Mathematics, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, Netherlands; email: r.fernandez1@uu.nl 
506 |2 openaire  |e Política editorial 
504 |a van Enter, A.C.D., Fernández, R., den Hollander, F., Redig, F., Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures (2002) Commun. Math. Phys., 226, pp. 101-130 
504 |a van Enter, A.C.D., On the prevalence of non-Gibbsian states in mathematical physics (2012) IAMP News Bull., 2012, pp. 15-24 
504 |a van Enter, A.C.D., Fernández, R., den Hollander, F., Redig, F., A large-deviation view on dynamical Gibbs-non-Gibbs transitions (2010) Moscow Math. J., 10, pp. 687-711 
504 |a Fernández, R., den Hollander, F., Martínez, J., Variational description of Gibbs-non-Gibbs dynamical transitions for the Curie-Weiss model (2013) Commun. Math. Phys., 319, pp. 703-730 
504 |a Külske, C., Le Ny, A., Spin-flip dynamics of the Curie-Weiss model: loss of Gibbsianness with possibly broken symmetry (2007) Commun. Math. Phys., 271, pp. 431-454 
504 |a Ermolaev, V., Külske, C., Low-temperature dynamics of the Curie-Weiss model: Periodic orbits, multiple histories, and loss of Gibbsianness (2010) J. Stat. Phys., 141, pp. 727-756 
504 |a Redig, F., Wang, F., Gibbs-non-Gibbs transitions via large deviations: computable examples (2012) J. Stat Phys., 147 (6), pp. 1094-1112 
504 |a den Hollander, F., Redig, F., van Zuijlen, W., (2013) Gibbs-non-Gibbs dynamical transitions for mean-field interacting Brownian motions, , arXiv, preprint arXiv: 1312. 3438 
504 |a Richard, K., (2014) Large deviations of the trajectory of empirical distributions of Feller processes on locally compact spaces, , arXiv, preprint arXiv: 1401. 2802 
504 |a Redig, F., Wang, F., (2013) Hamiltonian and Lagrangian for the trajectory of the empirical distribution and the empirical measure of Markov processes, , arXiv, preprint arXiv: 1311. 2282 
504 |a Dembo, A., Zeitouni, O., Large deviations techniques and applications (2010) Stochastic Modelling and Applied Probability, 38. , 2nd edn., Berlin: Springer 
504 |a Comets, F., Nucleation for a long range magnetic model (1987) Ann. Inst. H. Poincaré Probab. Stat., 23, pp. 135-178 
504 |a Comets, F., Eisele, T., Schatzman, M., On secondary bifurcations for some nonlinear convolution equations (1986) Trans. Am. Math. Soc., 296, pp. 661-702 
504 |a De Masi, A., Orlandi, E., Presutti, E., Triolo, L., Stability of the interface in a model of phase separation (1994) Proc. R. Soc. Edinb. A, 124, pp. 1013-1022 
504 |a Bates, P.W., Chen, X., Chmaj, A.J., Heteroclinic solutions of a van der Waals model with indefinite nonlocal interactions (2005) Calc. Var. Partial Differ. Equ., 24, pp. 261-281 
504 |a Yang, X., Integral convergence related to weak convergence of measures (2011) Appl. Math. Sci., 5, pp. 2775-2779 
504 |a Eisele, T., Ellis, R.S., Symmetry breaking and random waves for magnetic systems on a circle (1983) Z. Wahrsch. Verw. Gebiete, 63, pp. 297-348 
504 |a Drábek, P., Milota, J., (2007) Methods of Nonlinear Analysis: Applications to Differential Equations, , Basel: Birkhäuser 
504 |a Benois, O., Mourragui, M., Orlandi, E., Saada, E., Triolo, L., Quenched large deviations for Glauber evolution with Kac interaction and random field (2012) Markov Proc. Relat. Fields, 18, pp. 215-268 
504 |a Kipnis, C., Landim, C., Scaling limits of interacting particle systems (1999) Grundlehren Der Mathematischen Wissenschaften, 320. , Berlin: Springer 
520 3 |a 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.  |l eng 
536 |a Detalles de la financiación: VARIS-267356, BAPE-2009-1669 
536 |a Detalles de la financiación: Acknowledgments FdH is supported by ERC Advanced Grant VARIS-267356. JM is supported by Erasmus Mundus scholarship BAPE-2009-1669. The authors are grateful to A. van Enter and F. Redig for ongoing discussions on non-Gibbsianness, and to T. Franco and M. Jara for help with the hydrodynamic scaling argument in Appendix. 
593 |a Department of Mathematics, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, Netherlands 
593 |a Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, Netherlands 
593 |a Instituto de Investigaciones Matemáticas Luis A. Santaló, Conicet, C1428EGA Buenos Aires, Argentina 
690 1 0 |a ACTION INTEGRAL 
690 1 0 |a BIFURCATION OF RATE FUNCTION 
690 1 0 |a CURIE-WEISS MODEL 
690 1 0 |a DYNAMICAL TRANSITION 
690 1 0 |a GIBBS VERSUS NON-GIBBS 
690 1 0 |a KAC MODEL 
690 1 0 |a LARGE DEVIATION PRINCIPLES 
690 1 0 |a SPIN-FLIP DYNAMICS 
700 1 |a den Hollander, F. 
700 1 |a Martínez, J. 
773 0 |d Springer New York LLC, 2014  |g v. 156  |h pp. 203-220  |k n. 2  |p J. Stat. Phys.  |x 00224715  |w (AR-BaUEN)CENRE-379  |t Journal of Statistical Physics 
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856 4 0 |u https://doi.org/10.1007/s10955-014-1004-0  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_00224715_v156_n2_p203_Fernandez  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v156_n2_p203_Fernandez  |y Registro en la Biblioteca Digital 
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999 |c 84964 

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