Ferroelectric and dipolar glass phases of noncrystalline systems

In a recent Letter [Phys. Rev. Lett. 75, 2360 (1995)] we briefly discussed the existence and nature of ferroelectric order in positionally disordered dipolar materials. Here we report further results and give a complete description of our work. Simulations of randomly frozen and dynamically disordered dipolar soft spheres are used to study ferroelectric ordering in noncrystalline systems. We also give a physical interpretation of the simulation results in terms of short- and long-range interactions. Cases where the dipole moment has one, two, and three components (Ising, $\mathrm{XY}$, and $\mathrm{XYZ}$ models, respectively) are considered. It is found that the Ising model displays ferroelectric phases in frozen amorphous systems, while the $\mathrm{XY}$ and $\mathrm{XYZ}$ models form dipolar glass phases at low temperatures. In the dynamically disordered model the equations of motion are decoupled such that particle translation is completely independent of the dipolar forces. These systems spontaneously develop long-range ferroelectric order at nonzero temperature despite the absence of any fined-tuned short-range spatial correlations favoring dipolar order. Furthermore, since this is a nonequilibrium model, we find that the paraelectric to ferroelectric transition depends on the particle mass. For the $\mathrm{XY}$ and $\mathrm{XYZ}$ models, the critical temperatures extrapolate to zero as the mass of the particle becomes infinite, whereas for the Ising model the critical temperature is almost independent of mass, and coincides with the ferroelectric transition found for the randomly frozen system at the same density. Thus in the infinite mass limit the results of the frozen amorphous systems are recovered.