Dynamic scaling in the two-dimensional Ising spin glass with normal-distributed couplings

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Physics

Background:

• The two-dimensional Ising spin glass is a fundamental model in statistical mechanics.
• Understanding the dynamics of spin glasses near equilibrium transitions is crucial for materials science.
• Previous studies on bimodal couplings revealed anomalous relaxation behaviors.

Purpose of the Study:

• To investigate the dynamics of the 2D Ising spin glass with normal-distributed couplings.
• To test the generalized Kibble-Zurek scaling hypothesis in this system.
• To compare the relaxation dynamics with systems exhibiting bimodal couplings.

Main Methods:

• Simulated annealing was employed to explore the system's energy landscape.
• A generalized Kibble-Zurek scaling hypothesis was utilized to analyze the dynamics.
• Scaling analysis was performed at temperatures approaching absolute zero (T→0).

Main Results:

• An equilibrium glass transition was observed at temperature T=0.
• Power-law scaling was found for the velocity required to reach the ground state, v∼L^{-(z+1/ν)}.
• The dynamic critical exponent z was determined to be approximately 13.6, differing from systems with bimodal couplings.

Conclusions:

• Kibble-Zurek scaling is applicable to the 2D Ising spin glass with normal-distributed couplings.
• The unique ground state (up to spin reflection) contrasts with the massively degenerate states in bimodal systems, explaining differing dynamics.
• Quasidegenerate states likely cause the breakdown of perturbative behavior in the slow limit for continuous coupling distributions.