  We compare phase transition(-like) phenomena in small model systems for both
microcanonical and canonical ensembles. The model systems correspond to a few
classical (non-quantum) point particles confined in a one-dimensional box and
interacting via Lennard-Jones-type pair potentials. By means of these simple
examples it can be shown already that the microcanonical thermodynamic
functions of a small system may exhibit rich oscillatory behavior and, in
particular, singularities (non-analyticities) separating different microscopic
phases. These microscopic phases may be identified as different microphysical
dissociation states of the small system. The microscopic oscillations of
microcanonical thermodynamic quantities (e.g. temperature, heat capacity, or
pressure) should in principle be observable in suitably designed
evaporation/dissociation experiments (which must realize the physical
preconditions of the microcanonical ensemble). By contrast, singular phase
transitions cannot occur, if a small system is embedded into an infinite heat
bath (thermostat), corresponding to the canonical ensemble. For the simple
model systems under consideration, it is nevertheless possible to identify a
smooth canonical phase transition by studying the distribution of complex zeros
of the canonical partition function.
