  A model for two-dimensional colloids confined laterally by "structured
boundaries" (i.e., ones that impose a periodicity along the slit) is studied by
Monte Carlo simulations. When the distance D between the confining walls is
reduced at constant particle number from an initial value D_0, for which a
crystalline structure commensurate with the imposed periodicity fits, to
smaller values, a succession of phase transitions to imperfectly ordered
structures occur. These structures have a reduced number of rows parallel to
the boundaries (from n to n-1 to n-2 etc.) and are accompanied by an almost
periodic strain pattern, due to "soliton staircases" along the boundaries.
Since standard simulation studies of such transitions are hampered by huge
hysteresis effects, we apply the phase switch Monte Carlo method to estimate
the free energy difference between the structures as a function of the misfit
between D and D_0, thereby locating where the transitions occurs in
equilibrium. For comparison, we also obtain this free energy difference from a
thermodynamic integration method: the results agree, but the effort required to
obtain the same accuracy as provided by phase switch Monte Carlo would be at
least three orders of magnitude larger. We also show for a situation where
several "candidate structures" exist for a phase, that phase switch Monte Carlo
can clearly distinguish the metastable structures from the stable one. Finally,
applying the method in the conjugate statistical ensemble (where the normal
pressure conjugate to D is taken as an independent control variable) we show
that the standard equivalence between the conjugate ensembles of statistical
mechanics is violated.
