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Название: On the Two-Dimensional Dynamical Ising Model In the Phase Coexistence Region
Автор: Martinellil F.
We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of side L, in the absence of an external field and at large inverse temperature beta. We first consider the gap in the spectrum of the generator of the dynamics in two different cases : with plus and open boundary conditions. We prove that, when the symmetry under global spin flip is broken by the boundary conditions, the gap is much larger than the case in which the symmetry is present. For this latter we compute exactly the asymptotics of -(1/beta*L) log(gap) as L -> oo and show that it coincides with the surface tension along one of the coordinate axes. As a consequence we are able to study quite precisely the large deviations in time of the magnetization and to obtain an upper bound on the spin-spin time correlation in the infinite-volume plus phase.