94-294 Van Gulck S., Naudts J.

Non-equilibrium dynamics of the one-dimensional Glauber model (171K, TeX) Sep 21, 94

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Abstract. We study the relaxation of the one-dimensional Glauber model towards equilibrium at finite temperature, taking averages over all possible initial configurations. Let C(q,t) denote the spatial Fourier transform of the equal-time two-point correlation function <\sigma_0\sigma_n>_t. It can be written as the Laplace transform of a relaxation spectrum \rho_q(\omega). The latter turns out to contain a non-integrable singularity at a q-dependent frequency \omega=\theta(q). The singularity originates from the self-term in the equations of motion and has important consequences. E.g., it produces the dominating finite-size correction to C(q,t). As a consequence, we are able to formulate a finite-size scaling theory in the limit of zero temperature, long times and small wave vectors.

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