2D and 3D quantum rotors in a crystal field: critical points, metastability, and reentrance

Abstract

An overview of results of models of coupled quantum rotors is presented. We focus on rotors with dipolar and quadrupolar potentials in two and three dimensions, potentials which correspond to approximate descriptions of real molecules adsorbed on surfaces and in the solid phase. Particular emphasis is placed on the anomalous reentrant phase transition which occurs in both two and three-dimensional systems. The anomalous behaviour of the entropy, which accompanies the reentrant phase transition, is also analyzed and is shown to be present regardless if a phase transition is present or not. Finally, the effects of the crystal field on the phase diagrams are also investigated. In two-dimensions the crystal field causes the disappearance of the phase transition, and ordering takes place via a continuous increase in the value of the order parameter. This is also true in three dimensions for the dipolar potential. For the quadrupolar potential in three dimensions turning on the crystal field leads to the appearance of critical points where the phase transition ceases, and ordering occurs via a continuous increase in the order parameter. As the crystal field is increased the range of the coupling constant over which metastable states are found decreases.