PHASE ORDERING IN ONE-DIMENSIONAL SYSTEMS WITH LONG-RANGE INTERACTIONS

We study the dynamics of phase ordering of a nonconserved, scalar orde r parameter in one dimension, with long-range interactions characteriz ed by a power law r-d-sigma. In contrast to higher-dimensional systems , the point nature of the defects allows simpler analytic and numerica l methods. We find that, at least for sigma > 1, the model exhibits ev olution to a self-similar state characterized by a length scale which grows with time as t1/(1+sigma), and that the late-time dynamics is in dependent of the initial length scale. The insensitivity of the dynami cs to the initial conditions is consistent with the scenario of an att ractive, nontrivial renormalization-group fixed point which governs th e late-time behavior. For or less-than-or-equal-to 1 we find indicatio ns in both the simulations and an analytic method that this behavior m ay be dependent on system size.