Temperature Chaos, Rejuvenation and Memory in Migdal-Kadanoff Spin Glasses

TL;DR

This paper uses Migdal-Kadanoff simulations to explore temperature chaos, rejuvenation, and memory effects in spin glasses, revealing super-exponential decay of correlations and the conditions under which rejuvenation and memory occur.

Contribution

It provides new insights into the scales and mechanisms of rejuvenation and memory in spin glasses, especially regarding the role of temperature chaos and the overlap length.

Findings

Super-exponential decay of correlations in temperature chaos

Rejuvenation occurs below the overlap length scale

Memory persists even after extensive equilibration

Abstract

We use simulations within the Migdal-Kadanoff real space renormalization approach to probe the scales relevant for rejuvenation and memory in spin glasses. One of the central questions concerns the role of temperature chaos. First we investigate scaling laws of equilibrium temperature chaos, finding super-exponential decay of correlations but no chaos for the total free energy. Then we perform out of equilibrium simulations that follow experimental protocols. We find that: (1) rejuvenation arises at a length scale smaller than the ``overlap length'' l(T,T'); (2) memory survives even if equilibration goes out to length scales much larger than l(T,T').