Persistent Spins in the Linear Diffusion Approximation of Phase Ordering and Zeros of Stationary Gaussian Processes

1996/06/04 by Bernard Derrida, Vincent Hakim, Reuven Zeitak · 8 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Fractal and DNA sequence analysis #NMR spectroscopy and applications #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1103/physrevlett.77.2871

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

arxiv created 1996/06/04 · openalex publication_date 1996/09/30 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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 \ensuremathθ which depends on the space dimension. The dynamics is a special case of a stationary Gaussian process of known correlation function. The exponent \ensuremathθ 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 \ensuremathθ in close agreement with the results of simulations.

Citations

• Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models

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