Elisabetta Marcelli, Fabio Martinelli
Some new results on the 2d stochastic Ising model in the phase coexistence region.
(107K, plain TeX)
ABSTRACT. We consider a Glauber dynamics reversible with respect to the
two dimensional Ising model in a finite square of side $L$ with open boundary
conditions, in the absence of an external field and at large inverse temperature
$\beta$. 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
scale
$t_1$, much smaller than the global
relaxation time $t_o$, such that, with large probability, any initial configuration first
relaxes to one of the two \lq\lq phases" in a time scale of order $t_1$ and only
after a time scale of the order of $t_o$ it reaches 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.