AI Article Synopsis
- Studying low temperature spin glass models is tough due to slow dynamics and significant finite-size effects, but modern computational techniques can help overcome these challenges.
- Using advanced CPUs, researchers successfully simulated a four-dimensional Edwards-Anderson model up to a size of L=70, allowing for accurate measurements of its long-term behavior.
- By quenching various system sizes to critical temperatures, they found that finite-size effects become negligible at specific conditions, and their findings on dynamical and replicon exponents align with some theoretical frameworks but also show discrepancies with expected values.
Article Abstract
The study of the low temperature phase of spin glass models by means of Monte Carlo simulations is a challenging task, because of the very slow dynamics and the severe finite-size effects they show. By exploiting at the best the capabilities of standard modern CPUs (especially the streaming single instruction, multiple data extensions), we have been able to simulate the four-dimensional Edwards-Anderson model with Gaussian couplings up to sizes L=70 and for times long enough to accurately measure the asymptotic behavior. By quenching systems of different sizes to the critical temperature and to temperatures in the whole low temperature phase, we have been able to identify the regime where finite-size effects are negligible: ξ(t)≲L/7. Our estimates for the dynamical exponent (z≃1/T) and for the replicon exponent (α≃1.0 and T independent), that controls the decay of the spatial correlation in the zero overlap sector, are consistent with the replica symmetry breaking theory, but the latter differs from the theoretically conjectured value.
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| http://dx.doi.org/10.1103/PhysRevE.89.032127 | DOI Listing |
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