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

摘要: The study of the low temperature phase spin glass models by means Monte Carlo simulations is a challenging task, because very slow dynamics and severe finite-size effects they show. By exploiting at best capabilities standard modern CPUs (especially streaming single instruction, multiple data extensions), we have been able to simulate four-dimensional Edwards-Anderson model with Gaussian couplings up sizes $L=70$ for times long enough accurately measure asymptotic behavior. quenching systems different critical temperatures in whole phase, identify regime where are negligible: $\ensuremath{\xi}(t)\ensuremath{\lesssim}L/7$. Our estimates dynamical exponent ($z\ensuremath{\simeq}1/T$) replicon ($\ensuremath{\alpha}\ensuremath{\simeq}1.0$ $T$ independent), that controls decay spatial correlation zero overlap sector, consistent replica symmetry breaking theory, but latter differs from theoretically conjectured value.