PERSISTENT SPINS IN THE LINEAR DIFFUSION-APPROXIMATION OF PHASE ORDERING AND ZEROS OF STATIONARY GAUSSIAN-PROCESSES

The fraction r(t) of spins which have never flipped up to time t is st udied within a linear diffusion approximation to phase ordering. Numer ical simulations show that r(t) decays with time like a power law with a nontrivial exponent theta which depends on the space dimension. The dynamics is a special case of a stationary Gaussian process of known correlation function. The exponent theta is given by the asymptotic de cay of the probability distribution of intervals between consecutive z ero crossings. An approximation based on the assumption that successiv e zero crossings are independent random variables gives values of thet a in close agreement with the results of simulations.