Aging dynamics of +-J Edwards-Anderson spin glasses

TL;DR

This study uses extensive simulations to explore the aging dynamics of +-J Edwards-Anderson spin glasses in 4 and 6 dimensions, revealing distinct behaviors from Gaussian models and evidence of ultrametricity and super-aging at different temperatures.

Contribution

It provides new insights into the out-of-equilibrium dynamics of discrete energy level spin glasses, highlighting differences from continuous models and identifying scaling behaviors.

Findings

Discretization leads to interrupted aging behaviors.

At low temperatures, systems probe only the lowest energy levels.

Logarithmic scaling suggests ultrametricity in 4d at higher T.

Abstract

We analyze by means of extensive computer simulations the out of equilibrium dynamics of Edwards-Anderson spin glasses in d=4 and d=6 dimensions with +-J interactions. In particular, we focus our analysis on the scaling properties of the two-time autocorrelation function in a range of temperatures from T=0.07 T_c to T=0.75 T_c in both systems. We observe that the aging dynamics of the +-J models is different from that observed in the corresponding Gaussian models. In both the 4d and 6d models at very low temperatures we study the effects of discretization of energy levels. Strong interrupted aging behaviors are found. We argue that this is because in the times accessible to our simulations the systems are only able to probe activated dynamics through the lowest discrete energy levels and remain trapped around nearly flat regions of the energy landscape. For temperatures T >= 0.5 T_c in 4d we find logarithmic scalings that are compatible with dynamical ultrametricity, while in 6d the relaxation can also be described by super-aging scalings.