# Dynamic scaling in the 2D Ising spin glass with Gaussian couplings

## TL;DR

This study uses simulated annealing and Kibble-Zurek scaling to analyze the dynamic critical behavior of the 2D Gaussian-coupled Ising spin glass, revealing a large dynamic exponent and differences from bimodal coupling systems.

## Contribution

It provides the first detailed dynamic scaling analysis of the 2D Gaussian Ising spin glass, highlighting the impact of coupling distribution on relaxation dynamics.

## Key findings

- Dynamic critical exponent z=13.6 ± 0.4 for both order parameter and energy.
- Different relaxation behaviors compared to bimodal couplings due to ground state degeneracy.
- Kibble-Zurek scaling applies, but with altered scaling functions due to quasi-degenerate states.

## Abstract

We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature $T=0$. From a scaling analysis when $T\rightarrow 0$ at different annealing velocities, we extract the dynamic critical exponent $z$, i.e., the exponent relating the relaxation time $\tau$ to the system length $L$; $\tau\sim L^z$. We find $z=13.6 \pm 0.4$ for both the Edwards-Anderson spin-glass order parameter and the excess energy. This is different from a previous study of the system with bimodal couplings [S. J. Rubin, N. Xu, and A. W. Sandvik, Phys. Rev. E {\bf 95}, 052133 (2017)] where the dynamics is faster and the above two quantities relax with different exponents (and that of the energy is larger). We here argue that the different behaviors arise as a consequence of the different low-energy landscapes---for normal-distributed couplings the ground state is unique (up to a spin reflection) while the system with bimodal couplings is massively degenerate. 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 presented here indicate that, although Kibble-Zurek 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.