Aging in Spin Glasses in three, four and infinite dimensions

TL;DR

This study uses advanced simulations to analyze aging dynamics in spin glasses across three, four, and infinite dimensions, revealing deviations from expected models and challenging the ultrametricity hypothesis.

Contribution

It provides new empirical data on aging in spin glasses in multiple dimensions, highlighting deviations from traditional models and suggesting the need for revised theoretical frameworks.

Findings

Deviations from full-aging $t/t_w$ scaling are observed.

Evidence of multiple time sectors in aging dynamics.

Infinite-dimensional results challenge the ultrametricity hypothesis.

Abstract

The SUE machine is used to extend by a factor of 1000 the time-scale of previous studies of the aging, out-of-equilibrium dynamics of the Edwards-Anderson model with binary couplings, on large lattices (L=60). The correlation function, $C(t+t_w,t_w)$, $t_w$ being the time elapsed under a quench from high-temperature, follows nicely a slightly-modified power law for $t>t_w$. Very tiny (logarithmic), yet clearly detectable deviations from the full-aging $t/t_w$ scaling can be observed. Furthermore, the $t<t_w$ data shows clear indications of the presence of more than one time-sector in the aging 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 aging-properties are the same as for the spin correlation-function.