Kinetic Ising model in two and three dimensions with constraints

We present the dynamics of the kinetically constrained Ising model, comprised of a system of spins coupled with the strength J and situated in a field which plays the role of activation energy. Due to kinetic constraints, glassy effects arise at low temperatures leading to a non‐Arrhenius α ‐relaxation time. The results of Monte Carlo simulations are presented for the 2D and 3D facilitated kinetic Ising model with nonzero coupling J . The spin autocorrelation function exhibits, in a broad intermediate time regime, a pronounced stretched exponential decay characterized by an exponent γ . Whereas the relaxation time depends strongly on the activation energy and the interaction strength J , we find a non‐universal stretching exponent γ depending on the temperature and on J . In 3D the autocorrelation function shows a crossover into a pure exponential decay consistent with theoretical predictions. The magnetization is also analyzed and identified as a control parameter of the system. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)