Ageing in spin-glasses in three, four and infinite dimensions

The spin update engine (SUE) machine is used to extend, by a factor of 1000, the timescale of previous studies of the ageing, out-of-equilibrium dynamics of the Edwards–Anderson model with binary couplings, on large lattices (L = 60). The correlation function, C(t + tw, tw), tw being the time elapsed under a quench from high-temperature, follows nicely a slightly-modified power law for t > tw. Very small (logarithmic), yet clearly detectable deviations from the full-ageing t/tw scaling can be observed. Furthermore, the t < tw data show clear indications of the presence of more than one time sector in the ageing dynamics. Similar results are found in four dimensions, but a rather different behaviour is obtained in the infinite-dimensional z = 6 Viana–Bray model. Most surprisingly, our results in infinite dimensions seem incompatible with dynamical ultrametricity. A detailed study of the link correlation function is presented, suggesting that its ageing properties are the same as for the spin correlation function.