Generalized Competing Glauber-type Dynamics and Kawasaki-type Dynamics

In this article, we have given a systematic formulation of the new generalized competing mechanism: the Glauber-type single-spin transition mechanism, with probability p, simulates the contact of the system with the heat bath, and the Kawasaki-type spin-pair redistribution mechanism, with probability 1-p, simulates an external energy flux. These two mechanisms are natural generalizations of Glauber's single-spin flipping mechanism and Kawasaki's spin-pair exchange mechanism respectively. On the one hand, the new mechanism is in principle applicable to arbitrary systems, while on the other hand, our formulation is able to contain a mechanism that just directly combines single-spin flipping and spin-pair exchange in their original form. Compared with the conventional mechanism, the new mechanism does not assume the simplified version and leads to greater influence of temperature. The fact, order for lower temperature and disorder for higher temperature, will be universally true. In order to exemplify this difference, we applied the mechanism to 1D Ising model and obtained analytical results. We also applied this mechanism to kinetic Gaussian model and found that, above the critical point there will be only paramagnetic phase, while below the critical point, the self-organization as a result of the energy flux will lead the system to an interesting heterophase, instead of the initially guessed antiferromagnetic phase. We studied this process in details.Comment: 11 pages,1 figure

Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions

Autonomous multispecies systems with more-than-two-neighbor interactions are studied. Conditions necessary and sufficient for closedness of the evolution equations of the $n$-point functions are obtained. The average number of the particles at each site for one species and three-site interactions, and its generalization to the more-than-three-site interactions is explicitly obtained. Generalizations of the Glauber model in different directions, using generalized rates, generalized number of states at each site, and generalized number of interacting sites, are also investigated.Comment: 9 pages, LaTeX2