DYNAMICS AND DOMAIN-WALLS - IS THE LANDSCAPE PARADIGM INSTRUCTIVE

General questions concerning the dynamics of systems with many degrees of freedom are discussed, focussing on approach to equilibrium in sim ple statistical mechnical models. The contrasts between the behavior o f systems with short-range interactions and mean-field pictures in ter ms of energy ''landscapes'' are emphasized. It is shown how much of th e behavior of systems with short-range interactions can be described i n terms of domain walls and their dynamics. Simple Ising magnetic mode ls, both ferromagnets and spin glasses, are used as a paradigm.