WULFF DROPLETS AND THE METASTABLE RELAXATION OF KINETIC ISING-MODELS

We consider the kinetic Ising models (Glauber dynamics) corresponding to the infinite volume Ising model in dimension 2 with nearest neighbo r ferromagnetic interaction and under a positive external magnetic fie ld h. Minimal conditions on the flip rates are assumed, so that all th e common choices are being considered, We study the relaxation towards equilibrium when the system is at an arbitrary subcritical temperatur e T and the evolution is started from a distribution which is stochast ically lower than the (-)-phase. We show that as h SE arrow 0 the rela xation time blows up as exp(lambda(c)(T)/h), with lambda(c)(T) = w(T)( 2)/(12Tm(T)). Here m*(T) is the spontaneous magnetization and w(T) is the integrated surface tension of the Wulff body of unit volume. More over, for 0 < lambda < lambda(c), the state of the process at time exp (lambda/h) is shown to be close, when h is small, to the (-)-phase. Th e difference between this state and the (-)-phase can be described in terms of an asymptotic expansion in powers of the external held, This expansion can be interpreted as describing a set of C-infinity continu ations in h of the family of Gibbs distributions with the negative mag netic fields into the region of positive fields.