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.

In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair-correlation function. The critical characteristics of the dynamical relaxation tq, the complex susceptibility x(v,q), and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.

pin-1 model onto the spin-1/2 Ising model and have employed the exact results of the latter to find the exactly solvable cases of the spin-1 model. Our transformations are not one-to-one correspon-dences between Sf and Or and they are applicable to all lattices, depending on the lattice structure only through the coordination number. On square, triangle, and honeycomb lattices the exact critical points are shown in certain subspaces of parameter space (K, J, L, H, and△).

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.