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.