Dynamic scaling in the two-dimensional Ising spin glasses

We carry out simulated annealing and employ a generalized Kibble-Zurek (KZ) scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings [1]. From a scaling analysis when T→0 at different annealing velocities v, we find power-law scaling in the system size for the velocity required in order to relax toward the ground state; v∼ L^-(z+1/ν), where z is the dynamic exponent. We find z ≈13.6 for both the Edwards-Anderson order parameter and the excess energy. This is different from a previous study with bimodal couplings, where the dynamics is faster and the above two quantities relax with different dynamic exponents [2]. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results also indicate that, although KZ scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasi-degenerate states, and the scaling function takes a different form.
[1] Xu, et. al, PRE 96, 052102 (2017)
[2] Rubin, et. al, PRE 95, 052133 (2017)