Dynamic variational study of chaos: spin glasses in three dimensions

We have introduced a variational method to improve the computation of integrated correlation times in parallel tempering dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this determination of the correlation times, we revisited the problem of the characterization of the chaos in temperature in finite dimensional spin glasses, by way of the study of correlations between various chaos indicators computed in the static and the correlation times of the parallel tempering dynamics. The sample-distribution of the characteristic time for the parallel tempering dynamics turns out to be fat-tailed, and to obey finite-size scaling.