What the survivors' areas do at long times?

Abstract

We investigate the long time behavior of the survivors' area in the scaling state of two dimensional soap froth. We relate this problem to the recently studied temporal decay of the fraction of Potts spins that have never been flipped till time t. The results of our topological simulations are consistent with the value $\theta=1$ for the scaling exponent of the survivors' areas, in agreement with a recently obtained analytical result. We find, however, that the relaxation time needed to get into the scaling regime depends on the degree of randomness in the topological rearrangements and becomes very large in the deterministic limit.