Hard rotors on a lattice

Abstract: Many solids composed of non-spherical molecules show meso-phases: not a single transition from low temperature crystalline solid to a liquid with no crystalline order, but multiple intermediate phases, where the substance retains with a crystalline order, but varying degrees of orientational order. These mesophases are called plastic solids, or orientationally disordered crystals. I will discuss some recent work with J. Klamser, T. Sadhu and S. Saryal on a model where hard rigid rotors with some marked point on the rotor are fixed to the vertices of a d-dimensional lattice, but the rotors can adopt arbitrary orientations, subject to the condition that there is no overlap between different rotors. I will discuss the behavior of the system as the ratio �$\kappa$ of lattice constant to the size of the rotors is varied. It is found that the system undergoes multiple phase phase transitions as this ratio is varied. For some range of the �$\kappa$, the problem becomes reducible to the problem of determining entropy per site of the corresponding monomer- dimer model on the same lattice. The distribution function of the orientations shows cusp singularities, where the position and nature of the singularities can be determined exactly.

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