In this paper, we have exactly solved Glauber's critical dynamics of the Gaussian model in three dimensions. Of course, it is much easier to apply in the low-dimensional case. The key steps are that we generalize the spin change mechanism from Glauber's single-spin flipping to single-spin transition and give a normalized version of the transition probability. We have also investigated the dynamical critical exponent and found surprisingly that the dynamical critical exponent is highly universal; that is, for one, two, and three dimensions they have the same value independent of spatial dimensionality in contrast to static ~equilibrium! critical exponents.

A surface reaction model, the Ziff-Gulari-Barshad model, is studied on fractal lattices by the Monte Carlo method, and the influence of the lacunarity of the lattice on the dynamic scaling properties of the continuous transition in the model is investigated. The dynamic critical exponents are obtained on different lattices. We find that the transitions in the model on fractal lattices with different lacunarity do not belong to the same universality class.

We study the aggregation-annihilation processes involving three or more kinds of distinct monomers species based on mean-field theory. We propose several solvable models in which irreversible bonding occurs only between similar species and annihilation occurs only between dissimilar species. Under constant aggregation and annihilation reaction rates, the exact solutions of these models are obtained. These analytical solutions show that the kinetic evolution behaviors of each species are quite different. They are scaling or nonscaling depending conclusively on all reaction rates and initial mass distribution of each of the reactants.

We have studied the kinetic phase transition of a three-state-vector Potts system on a triangular lattice in contact with a heat bath and subject to an external energy source. The system evolves via the stochas-tic dynamics composed of Glauber and Kawasaki dynamics simulating interaction with the heat bath and energy source, respectively. The pair approximation IS used. It 1S found that there IS a paramagnetic-ferromagnetic transition at small energy flow, and the transition line is obtained. Also, when the energy is large enough, the system always will be in the paramagnetic state.

We have studied quadric type energy (frequency) recursion relations resulting from fractal lattices. We found that the allowed energy intervals in successive levels form two similar two-scale Cantor sets. If WE imagine the iterating procedure as a dynamical process, the iterating results in different levels gen-erate a"time"sequence, and we can introduce an equal probability measure Pu on a Cantor set and con-struct，following Helsey et a1. [Phys. Rev. A 33, 1141 (1986)], a partition function F (q,T) =∑ipq/17; finally, we obtain Dq-q and f (a)-a curves. A number of exactly soluable examples are investigated.