Static and dynamic phase transitions in multidimensional voting models on continua.
A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice, each site of which is either empty or occupied by a single particle. The reactions of the system are such that two adjacent sites, one empty, the other occupied, may evolve to a state where both of these sites are either empty or occupied. The continuum version of this model in a D-dimensional region with a boundary is studied, and two general behaviors of such systems are investigated, the stationary behavior of the system, and the dominant way of relaxation of the system toward its stationary state. Based on the first behavior, a static phase transition (discontinuous changes in the stationary profiles of the system) is studied. Based on the second behavior, a dynamical phase transition (discontinuous changes in the relaxation times of the system) is studied. It is shown that the static phase transition is induced by the bulk reactions only, while the dynamical phase transition is a result of both bulk reactions and boundary conditions.
Roshani
F
F
Institute for Advanced Studies in Basic Sciences, P.O. Box 159, Zanjan 45195, Iran. farinaz@iasbs.ac.ir
Aghamohammadi
A
A
Khorrami
M
M