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 studied within a linear diffusion approximation to phase ordering. Numerical 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 decay of the probability distribution of intervals between consecutive zero crossings. An approximation based on the assumption that successive zero crossings are independent random variables gives values of theta in close agreement with the results of simulations.