Spatial correlation functions and dynamical exponents in very large samples of four-dimensional spin glasses

Area of Science:

• Condensed Matter Physics
• Computational Physics

Background:

• Spin glass models exhibit slow dynamics and finite-size effects at low temperatures, complicating simulations.
• Accurate simulation of these models requires overcoming computational challenges.

Purpose of the Study:

• To perform large-scale Monte Carlo simulations of the four-dimensional Edwards-Anderson model.
• To accurately measure asymptotic behavior and critical exponents in the low-temperature phase.
• To identify the regime where finite-size effects become negligible.

Main Methods:

• Utilized modern CPUs with Single Instruction, Multiple Data (SIMD) extensions for efficient computation.
• Performed Monte Carlo simulations on the four-dimensional Edwards-Anderson model with Gaussian couplings.
• Quenched systems of various sizes to critical and low temperatures to analyze dynamics.

Main Results:

• Simulated systems up to size L=70, achieving sufficient simulation times for asymptotic behavior analysis.
• Identified the finite-size scaling regime as ξ(t)≲L/7.
• Estimated the dynamical exponent (z≃1/T) and replicon exponent (α≃1.0, T-independent).

Conclusions:

• The simulation results are consistent with replica symmetry breaking theory.
• The estimated replicon exponent differs from the theoretically conjectured value, suggesting further investigation.