Correlations in Space and Time for a Soft-mode Phase-transforming System

Abstract

Using molecular dynamics (MD) for a system of.nonlinear (quadruple-quadratic) oscillators on a nearest-neighbour square lattice, the pair-displacement correlations. and the frequency spectrum for the dynamical order-parameter correlation function are obtained as a function of temperature. For temperatures T near Tc' the pair-displacement correlation function (with the long-range order component subtracted out) was found to vary with particle separation r as r- 1/2 exp { - A( T) rj, at least out to the tenth neighbour in the 40x40 particle lattice. This is consistent with predictions for the two-dimensional Ising model for T above, but not below, Tc. The frequency spectrum for the dynamical order-parameter correlation function shows the softening of the damped phonon-like modes as T approaches Tc and the formation of a central peak at Tc' consistent with the presence of soliton-like excitations. For small I T - Tc I an additional broad peak appears at low frequencies. This is interpreted as an additional phonon-like peak, the two quasi-phonon processes being associated with vibration across the potential barrier and vibration in one or other of the two potential wells respectively. Although the squared frequency wi of the soft quasi-phonon is approximately linear with I T - Tc lover a range of temperatures, as T increases the wi curve eventually flattens out.