Small-World Network Effect in Competing Glauber- and Kawasaki-type Dynamics

In this article, we investigate the competing Glauber-type and Kawasaki-type dynamics with small-world network (SWN) effect, in the framework of the Gaussian model. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. Two different types of SWN effect are studied, one with the total number of links increased and the other with it conserved. The competition of the dynamics leads to an interesting self-organization process that can be characterized by a phase diagram with two identifiable temperatures. By studying the modification of the phase diagrams, the SWN effect on the two dynamics is analyzed. For the Glauber-type dynamics, more important is the altered average coordination number while the Kawasaki-type dynamics is enhanced by the long range spin interaction and redistribution.Comment: 18 pages, 1 figure. Accepted for publication in "The European Physical Journal B (EPJB)

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

Kawasaki-type Dynamics: Diffusion in the kinetic Gaussian model

In this article, we retain the basic idea and at the same time generalize Kawasaki's dynamics, spin-pair exchange mechanism, to spin-pair redistribution mechanism, and present a normalized redistribution probability. This serves to unite various order-parameter-conserved processes in microscopic, place them under the control of a universal mechanism and provide the basis for further treatment. As an example of the applications, we treated the kinetic Gaussian model and obtained exact diffusion equation. We observed critical slowing down near the critical point and found that, the critical dynamic exponent z=1/nu=2 is independent of space dimensionality and the assumed mechanism, whether Glauber-type or Kawasaki-type.Comment: accepted for publication in PR