Kinetic Ashkin-Teller model with competing dynamics

Damage spreading in two-dimensional trivalent cellular structures with competing Glauber and Kawasaki dynamics

The damage spreading of the Ising model on several two-dimensional trivalent structures, including soap froth, Voronoi, and hierarchical structures, are studied with competing Glauber and Kawasaki dynamics. The damage spreading transition temperature T(d) and the Curie temperature T(C) of these structures are compared. We find that T(d) of the hierarchical lattices decreases sharply as the probability of occurrence of Kawasaki dynamics increases, whereas for soap froth and Voronoi, T(d) for the Voronoi and soap froth remain nearly unchanged except when the dynamics is dominated by Kawasaki dynamics. T(d) and T(C) in our two-dimensional structures are nearly the same and they behave similarly as we change the relative probability of occurrence of the Glauber and Kawasaki dynamics. A heuristic argument is provided to explain the numerical results.

One-dimensional Ising model built on small-world networks: competing dynamics

In this paper, we offer a competing dynamic analysis of the one-dimensional Ising model built on the small-world network (SWN). Adding-type SWNs are investigated in detail using a simplified Hamiltonian of mean-field nature, and the result of rewiring-type is given because of the similarities of these two typical networks. We study the dynamical processes with competing Glauber mechanism and Kawasaki mechanism. 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. By studying the phase diagram obtained in the present work, we can realize some dynamical properties influenced by the small-world effect.

Nonequilibrium antiferromagnetic mixed-spin Ising model

We studied an antiferromagnetic mixed-spin Ising model on the square lattice subject to two competing stochastic processes. The model system consists of two interpenetrating sublattices of spins sigma=1/2 and S=1, and we take only nearest neighbor interactions between pairs of spins. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip (Glauber dynamics). Besides, the system interacts with an external agency of energy, which supplies energy to it whenever two nearest neighboring spins are simultaneously flipped. By employing Monte Carlo simulations and a dynamical pair approximation, we found the phase diagram for the stationary states of the model in the plane temperature T versus the competition parameter between one- and two-spin flips p. We observed the appearance of three distinct phases, that are separated by continuous transition lines. We also determined the static critical exponents along these lines and we showed that this nonequilibrium model belongs to the universality class of the two-dimensional equilibrium Ising model.

Generalized competing Glauber-type dynamics and Kawasaki-type dynamics

In this paper, we have given a systematic formulation of a 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 proposed 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 proposed mechanism does not assume the simplified version and leads to a 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 the one-dimensional Ising model and obtained analytical results. We also applied this mechanism to the 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.