Some new results on the two-dimensional kinetic Ising model in the phase coexistence region

Abstract

We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL with open boundary conditions, in the absence of an external field and at large inverse temperature β. We prove that the gap in the spectrum of the generator restricted to the invariant subspace of functions which are even under global spin flip is much larger than the true gap. As a consequence we are able to show that there exists a new time scaleteven, much smaller than the global relaxation timetrel, such that, with large probability, any initial configuration first relaxes to one of the two “phases” in a time scale of orderteven and only after a time scale of the order oftrel does it reach the final equilibrium by jumping, via a large deviation, to the opposite phase. It also follows that, with large probability, the time spent by the system during the first jump from one phase to the opposite one is much shorter than the relaxation time.