Dynamics of structural phase transitions in highly anisotropic systems

We report computer simulations of a two-dimensional (2D) highly anisotropic lattice-dynamical model which exhibits a structural phase transition. The model is a set of chains weakly coupled by harmonic forces; within each chain the particles move in a double minimum ${\phi }^4$ potential with harmonic interparticle coupling. For the simulations here, the ratio of the coupling constants in the two directions is 400:1. We present numerical results for thermodynamic properties which confirm that the system has a second-order phase transition. The major emphasis of the simulation is on dynamic properties, however. We employ a graphical device (‘‘soliton detector’’) which gives a coarse-grained pictorial representation of the particle motions. Further, we present extensive calculations of wave-vector- and frequency-dependent spectral functions of displacement fluctuations. The order parameter (q=0) spectral function has a soft-mode peak and a central peak, as seen in scattering experiments. A major result of these calculations is that the minimum soft-mode frequency occurs at a (soft-mode) temperature $T_s$ which is considerably above the critical temperature $T_c$. This soft-mode temperature can be correlated with the appearance of one-dimensional soliton propagation along the chains. The critical temperature is related to the growth of 2D correlations resulting from the interchain coupling. These 2D fluctuations are responsible for a dramatic narrowing and intensity increase of the central peak in the 2D system as compared to the corresponding 1D system. We conclude with calculations of the effects of interactions between solitons on neighboring chains and how such correlations would be manifested in the spectral functions.