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)similar t oL(-z theta)f(t/L-z), where theta is the persistence exponent and z is the coarsening exponent. The scaling function f(x)similar tox(-theta) for x<<1 and is constant for large x. The scaling form implies a fractal distributio n of persistent sites with power-law spatial correlations. We study the sca ling numerically for the Glauber-Ising model at dimension d = 1 to 4 and ex tend the study to the diffusion problem. Our finite-size scaling ansatz is satisfied in all these cases providing a good estimate of the exponent thet a.