The decay of the Hamming distance in Monte Carlo simulations of Ising models with model A dynamics is shown to be numerically efficient to investigate the dynamics also below T~.. We observe a simple exponential decay in three and four dimensions below and above the Curie temperature. In two dimensions, a stretched exponential decay is observed only below To. The exponent in the latter is between the two predictions of Takano et al. and Huse and Fisher, but the dynamics of single droplets is clearly found to disagree with Takano et al.
During the last decade the method of damage spreading [ 1-7] has been widely used to investigate time-dependent critical phenomena. Damage spreading is a technique where two identical lattices are simulated with different initial conditions but with the same sequence of random numbers. If the spin difference (the "damage") decreases to zero, then the system is "stable" in the sense that it does not show sensitive dependence with respect to initial conditions for a fixed realization of the random number sequence. We speak in this case of damage healing. In the opposite case where a small initial damage spreads, the system can be considered to be chaotic.
The detailed properties with respect to damage depend strongly on the used Monte Carlo scheme. Thus it seems that in the Glauber dynamics of the Ising model there is a damage spreading transition which does not coincide with the critical temperature [8,9], and which is in the directed percolation universality class . The situation is completely different for heat bath dynamics (for the implementation of heat bath dynamics for lattice pairs involved in this statement, see ), as explained theoretically