Dynamical scaling from multiscale measurements

We present a measure of the dynamical critical behavior: the multiscale dynamical exponent (MDE), zmd. Using dynamical renormalization-group concepts we study the relaxation times, , of a family of space scales defined by =1/k. Assuming dynamical universality we argue, and verify numerically, that zmd has the same value as the usually defined z. We measure zmd in the two-dimensional Ising model with the Metropolis and cluster dynamics and find zmetmd=2.1 0.1 and zwolffmd=0 0.15, respectively. We note that in our approach zmd is measured using a single temperature and a single lattice size. In addition, in the Metropolis case we present a method which helps to overcome critical slowing down in the dynamical measurements themselves.