COLLECTIVE DEGREES OF FREEDOM AND MULTISCALE DYNAMICS IN SPIN-GLASSES

We relate the long-range, long-time correlations during the simulation of disordered complex systems to the relevant macroscopic effective c ollective degrees of freedom. We prove that in systems that have an ul trametric space of ground states, the tunneling between vacuums cannot be expressed in terms of spatially disjoint clusters or in terms of s patial multiscale hierarchies. We relate this to the ultraslow converg ence difficulties of multiscale-cluster algorithms in such systems; On the contrary, in the case of finite connectivity (dilute) spin glasse s, we are able to find multiscale-cluster algorithms that are much mor e efficient than the usual methods. We relate their efficiency explici tly to their action on specific collective degrees of freedom. These d egrees of freedom are responsible for the slowing down of the usual al gorithms.