Persistence in higher dimensions: A finite size scaling study

We show that the persistence probability P(t,L), in a coarsening system of linear size L at a time t, has the finite-size scaling form P(t,L) approximately L(-zstraight theta)f(t/L(z)), where straight theta is the persistence exponent and z is the coarsening exponent. The scaling function f(x) approximately x(-straight theta) for x<<1 and is constant for large x. The scaling form implies a fractal distribution of persistent sites with power-law spatial correlations. We study the scaling numerically for the Glauber-Ising model at dimension d=1 to 4 and extend the study to the diffusion problem. Our finite-size scaling ansatz is satisfied in all these cases providing a good estimate of the exponent straight theta.