Dynamical phase transition in one-dimensional kinetic Ising model with nonuniformcoupling constants

Abstract

An extension of the kinetic Ising model with nonuniform coupling constants on aone-dimensional lattice with boundaries is investigated, and the relaxation of such a systemtowards its equilibrium is studied. Using a transfer matrix method, it is shown that thereare cases where the system exhibits a dynamical phase transition. There may be twophases, the fast phase and the slow phase. For some region of the parameterspace, the relaxation time is independent of the reaction rates at the boundaries.Changing continuously the reaction rates at the boundaries, however, there is a pointwhere the relaxation time begins changing as a continuous (nonconstant) functionof the reaction rates at the boundaries, so that at this point there is a jump inthe derivative of the relaxation time with respect to the reaction rates at theboundaries.