3 years ago

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

Ying-Jer Kao, Kai-Hsin Wu, Na Xu, Shanon J. Rubin, Anders W. Sandvik

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.

Publisher URL: http://arxiv.org/abs/1706.05472

DOI: arXiv:1706.05472v2

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