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An overview of results of models of coupled quantum rotors is presented. Wefocus on rotors with dipolar and quadrupolar potentials in two and threedimensions, potentials which correspond to approximate descriptions of realmolecules adsorbed on surfaces and in the solid phase. Particular emphasis isplaced on the anomalous reentrant phase transition which occurs in both two andthree-dimensional systems. The anomalous behaviour of the entropy, whichaccompanies the reentrant phase transition, is also analyzed and is shown to bepresent regardless if a phase transition is present or not. Finally, theeffects of the crystal field on the phase diagrams are also investigated. Intwo-dimensions the crystal field causes the disappearance of the phasetransition, and ordering takes place via a continuous increase in the value ofthe order parameter. This is also true in three dimensions for the dipolarpotential. For the quadrupolar potential in three dimensions turning on thecrystal field leads to the appearance of critical points where the phasetransition ceases, and ordering occurs via a continuous increase in the orderparameter. As the crystal field is increased the range of the coupling constantover which metastable states are found decreases.

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