Spin models for orientational ordering of colloidal molecular crystals

Two-dimensional colloidal suspensions exposed to periodic external fields exhibit a variety of molecular crystalline phases. There two or more colloids assemble at lattice sites of potential minima to build new structural entities, referred to as molecules. Using the strength of the potential and the filling fraction as control parameters, a phase transition to unconventional orientationally ordered states can be induced. We introduce an approach that focuses at the discrete set of orientational states relevant for the phase ordering. The orientationally ordered states are mapped to classical spin systems. We construct effective Hamiltonians for dimeric and trimeric molecules on triangular lattices suitable for a statistical mechanics discussion. A mean-field analysis produces a rich phase behavior which is substantiated by Monte Carlo simulations.