Molecular-dynamics study of structural-phase transitions. I. One-component displacement models

Abstract

Molecular-dynamics results simulating a canonical ensemble are presented and discussed for a two-dimensional one-component displacement model for ferrodistortive and antiferrodistortive structural-phase transitions. Our results include: (i) There is strong evidence that the system undergoes a continuous phase transition, except at the displacive limit. (ii) For three different sets of model paramerters, the static critical exponents are found to be model parameters independent and consistent with those of the two-dimensional Ising model. (iii) The formation of clusters of locally ordered regions is demonstrated. (iv) Close to ${T}_{c}$ and at the wave vector ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{c}$ where the order-parameter susceptibility diverges, we observe a central peak around $\ensuremath{\omega}=0$ in the dynamic form factor of the density fluctuations. (v) For wave vectors slightly away from ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{c}$ the central peak splits into a double-peak structure, giving rise to a new excitation branch. (vi) The central peak and the new excitation branch are traced back to traveling cluster waves and their lifetime. (vii) The cluster dynamics is shown to dominate the critical slowing down.