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Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models

J. Kisker·L. Santen·M. Schreckenberg·H. Rieger
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Abstract

The low temperature dynamics of the two- and three-dimensional Ising spin glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the autocorrelation function $C(t,t_w)=[< S_i(t+t_w)S_i(t_w)>]_{av}$ a typical aging scenario with a $t/t_w$ scaling is established. Investigating spatial correlations we find an algebraic growth law $ξ(t_w)\sim t_w^{α(T)}$ of the average domain size. The spatial correlation function $G(r,t_w)=[< S_i(t_w)S_{i+r}(t_w)>^2]_{av}$ scales with $r/ξ(t_w)$. The sensitivity of the correlations in the spin glass phase with respect to temperature changes is examined by calculating a time dependent overlap length. In the two dimensional model we examine domain growth with a new method: First we determine the exact ground states of the various samples (of system sizes up to $100\times 100$) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation.

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J. Kisker, L. Santen, M. Schreckenberg, H. Rieger. 1995-07-13. Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models. https://doi.org/10.1103/physrevb.53.6418

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