Search

The critical dynamics of the Glauber-Ising model on nontranslationally invariant lattices is studied. Both a quasi-periodic and a fractal geometry are considered. The distribution of inverse relaxation times rho (1/ tau ) is calculated using a generating function method. The distribution consists of bands with an internal self-similar structure. In the limit 1/ tau to 0, rho (1/ tau ) diverges with a universal exponent related to the dynamic critical exponent z. The width of the lowest frequency band is determined by a nonuniversal bare time scale, which is related to the presence of metastable states.

The authors examine, by Monte Carlo simulation and the damage algorithm, the late-time behaviour of fluctuations in the low-temperature ordered phase of the two-dimensional kinetic Ising model. It has been suggested that at late-times correlations could be dominated by long-lived droplet fluctuations of the other ordered phase, giving rise to stretched-exponential decays of the spin auto-correlation function. Over the time regimes they have studied, they see no evidence for anomalous long-lived droplets and find that the probability distribution for droplet lifetimes decays by an ordinary exponential.

It is shown that Glauber dynamics in 1D Ising spin systems is not universal. This is illustrated on a periodic model with a basic unit cell (J1,. . ., Jn) containing an arbitrary set of n ferromagnetic coupling constants. The dynamic critical exponent z is calculated exactly as z=1+max(Ji)/min(Ji), the known value z=2 is recovered only for n=1. The extension of this result to other types of dynamics is briefly discussed.

One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent $\Theta$ and the exponent $lambda$ characterising the two-time autocorrelation function of the total magnetization under non-equilibrium conditions are reported. It is found that the PC transition has strong effect: the process becomes non-Markovian and the above exponents exhibit drastic changes as compared to the Glauber-Ising case.

For cellular automata versions of Glauber and Metropolis kinetic Ising models in one dimension the critical and domain growth dynamical exponents, Zcr and Zdg are shown to coincide if the dynamical scaling assumption holds. Computer simulations presented yield Zdg=Zcr equal to 2 and 1, respectively, for the Glauber and Metropolis models with checkerboard updating. The latter model with its faster relaxation is suggested as an algorithm superior to the usual Monte Carlo ones.

The author presents an investigation of the dynamic critical behaviour near the percolation bicritical point of the 1D bond-diluted Glauber Ising model. The expected bicritical dynamic scaling form is rigorously established for the decay functions describing the decay of the equilibrium wavevector-dependent correlation function and the decay of the magnetisation from a (non-equilibrium) wavevector-dependent initial state. The corresponding characteristic decay times are evaluated exactly and exhibit a cross over from 'pure' to percolation dominated behaviour on increasing the dilution. The results in the percolation regime are in agreement with recent calculations in which domain boundary diffusion methods are applied to a wider class of kinetic Ising models.

A time-dependent real-space renormalisation group is used to show that all the one-dimensional kinetic Ising models with transition rate that depends on nearest neighbours only belong to the same universality glass of the critical dynamics.