Asymptotic Exponential Law for the Transition Time to Equilibrium of the Metastable Kinetic Ising Model with Vanishing Magnetic Field

Autor: Maria Eulália Vares, Paolo Milanesi, Alexandre Gaudillière
Přispěvatelé: Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Instituto de Matemática da Universidade Federal do Rio de Janeiro (IM / UFRJ), Universidade Federal do Rio de Janeiro (UFRJ), M. E. V. acknowledges partial support of CNPq (grant 305075/2016-0) and Faperj E-26/203.948/2016., Instituto de Matemática (UFRJ), Universidade Federal do Rio de Janeiro [Rio de Janeiro] (UFRJ)
Rok vydání: 2020
Předmět:
Zdroj: Journal of Statistical Physics
Journal of Statistical Physics, 2020, 179 (2), pp.263-308. ⟨10.1007/s10955-019-02463-5⟩
Journal of Statistical Physics, Springer Verlag, 2020, 179 (2), pp.263-308. ⟨10.1007/s10955-019-02463-5⟩
ISSN: 1572-9613
0022-4715
DOI: 10.1007/s10955-019-02463-5
Popis: International audience; We consider a Glauber dynamics associated with the Ising model on a large two-dimensional box with with minus boundary conditions and in the limit of a vanishing positive external magnetic field. The volume of this box increases quadratically in the inverse of the magnetic field. We show that at subcritical temperature and for a large class of starting measures, including measures that are supported by configurations with macroscopic plus-spin droplets, the system rapidly relaxes to some metastable equilibrium ---with typical configurations made of microscopic plus-phase droplets in a sea of minus spins--- before making a transition at an asymptotically exponential random time towards equilibrium ---with typical configurations made of microscopic minus-phase droplets in a sea of plus spins inside a large contour that separates this plus phase from the boundary. We get this result by bounding from above the local relaxation times towards metastable and stable equilibria. This makes possible to give a pathwise description of such a transition, to control the asymptotic behaviour of the mixing time in terms of soft capacities and to give estimates of these capacities.
Databáze: OpenAIRE
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