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

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: xi(t) less than or similar to L/7. Our estimates for the dynamical exponent (z similar or equal to 1/T) and for the replicon exponent (alpha similar or equal to 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.