Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes

Details Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes

1996-06-03

arxiv.org/abs/cond-mat/9606005v2

Physics

Condensed Matter

10 pages, 2 postscript files. Submitted to PRL. Reference screwup corrected

Scientific paper

10.1103/PhysRevLett.77.2871

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, even in this simple context, r(t) decays with time like a power-law with a non-trival exponent $\theta$ which depends on the space dimension. The local dynamics at a given point is a special case of a stationary gaussian process of known correlation function and the exponent $\theta$ is shown to be determined by the asymptotic behavior of the probability distribution of intervals between consecutive zero-crossings of this process. An approximate way of computing this distribution is proposed, by taking the lengths of the intervals between successive zero-crossings as independent random variables. The approximation gives values of the exponent $\theta$ in close agreement with the results of simulations.

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