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Variational description of Gibbs-non-Gibbs dynamical transitions for spin-flip systems with a Kac-type interaction
- Publication Year :
- 2013
-
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 \cite{vEFedHoRe10}, in the thermodynamic limit Gibbs-non-Gibbs dynamical transitions are \emph{equivalent} to bifurcations in the set of global minima of the large-deviation rate function for the trajectories of the empirical density \emph{conditional} on their endpoint. More precisely, the time-evolved measure is non-Gibbs if and only if this set is not a singleton for \emph{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.<br />Comment: Key words and phrases: Curie-Weiss model, Kac model, spin-flip dynamics, Gibbs versus non-Gibbs, dynamical transition, large deviation principles, action integral, bifurcation of rate function
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1309.3667
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10955-014-1004-0