Dynamic scaling in the two-dimensional Ising spin glass with normal-distributed couplings
Journal
Physical Review E
Journal Volume
96
Journal Issue
5
Date Issued
2017
Author(s)
URI
Abstract
We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the two-dimensional Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature T=0. 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), the Kibble-Zurek ansatz where z is the dynamic critical exponent and ν the previously known correlation-length exponent, ν≈3.6. We find z≈13.6 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 [Rubin et al., Phys. Rev. E 95, 052133 (2017)2470-004510.1103/PhysRevE.95.052133] where the dynamics is faster (z is smaller) and the above two quantities relax with different dynamic exponents (with that of the energy being larger). We 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 also indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasidegenerate states, and the scaling function takes a different form. © 2017 American Physical Society.
SDGs
Other Subjects
Couplings; Glass; Glass transition; Ground state; Ising model; Simulated annealing; Continuous couplings; Correlation lengths; Dynamic critical exponents; Energy landscape; Power law scalings; Relaxation behaviors; Scaling analysis; Scaling functions; Spin glass
Type
journal article