Configuration Memory in Patchwork Dynamics for Low-dimensional Spin Glasses

A patchwork method is used to study the dynamics of loss and recovery of an initial configuration in spin glass models in dimensions d = 1 and d = 2. The patchwork heuristic is used to accelerate the dynamics to investigate how models might reproduce the remarkable memory effects seen in experiment. Starting from a ground state configuration computed for one choice of nearest neighbor spin couplings, the sample is aged up to a given scale under new random couplings, leading to the partial erasure of the original ground state. The couplings are then restored to the original choice and patchwork coarsening is again applied, in order to assess the recovery of the original state. Eventual recovery of the original ground state upon coarsening is seen in two-dimensional Ising spin glasses and one-dimensional Potts models, while one-dimensional Ising glasses neither lose nor gain overlap with the ground state during the recovery stage. The recovery for the two-dimensional Ising spin glasses suggests scaling relations that lead to a recovery length scale that grows as a power of the aging length scale.