Critical slowing down in local dynamics simulations

The author reports some universal and non-universal aspects of the critical dynamics of the three-dimensional Ising model, obtained in extensive Monte Carlo finite-size simulations. The author shows that the time-dependence of the magnetization of finite lattices is composed of two kinds of fluctuations at the critical point: (i) phase fluctuations from one metastable minimum of the free energy to the other, dominating the long-time behaviour of the magnetization; (ii) critical fluctuations inside each minimum, decaying on a comparatively short timescale. Both kinds of fluctuations show up the same critical exponent z=2.10+or-0.02, which is also in excellent agreement with the exponent z of energy fluctuations.