Dynamic structure factor of the Ising model with purely relaxational dynamics

Calabrese, P. and Martin-Mayor, V. and Pelissetto, A. and Vicari, E. (2003) Dynamic structure factor of the Ising model with purely relaxational dynamics. Physical review. E, Statistical, nonlinear, and soft matter physics, 68 . 016110. ISSN 1550-2376

Abstract

We compute the dynamic structure factor for the Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the $\epsilon$ expansion, at two loops in the high-temperature phase and at one loop in the temperature magnetic-field plane, and a Monte Carlo simulation in the high-temperature phase. We find that the dynamic structure factor is very well approximated by its mean-field Gaussian form up to moderately large values of the frequency $\omega$ and momentum $k$. In the region we can investigate, $k\xi \lesssim 5$, $\omega \tau \lesssim 10$, where $\xi$ is the correlation length and $\tau$ the zero-momentum autocorrelation time, deviations are at most of a few percent.

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