L. Chayes et al., LIFSHITZ LAW FOR THE VOLUME OF A 2-DIMENSIONAL DROPLET AT ZERO-TEMPERATURE, Journal of statistical physics, 79(5-6), 1995, pp. 821-831
We study a simple model of the zero-temperature stochastic dynamics fo
r interfaces in two dimensions--essentially Glauber dynamics of the tw
o-dimensional Ising model at T = 0. Using elementary geometric conside
rations, we show that the (rescaled) volume of an initially square dro
plet decreases linearly to zero as a function of (rescaled) time.