The relaxation to equilibrium in one-dimensional potts models

Abstract

For both spin-conserving and nonconserving dynamics, an overview is given of the studies of relaxation to equilibrium in one-dimensional kinetic Potts models with only the nearest neighbor couplings at low temperature. The Potts model shows coarsening for ferromagnetic couplings, with typical size of domains increasing with time. The state of the system for antiferromagnetic couplings in the limit of large times is not stationary; the system jumps between the large number of degenerate ground states. A large variety of relaxation is seen. Briefly summarized are some new results for the q = 3 antiferromagnetic Potts model under Glauber and Kawasaki dynamics.