  In contrast to the canonical ensemble where thermodynamic functions are
smooth for all finite system sizes, the microcanonical entropy can show
nonanalytic points also for finite systems, even if the Hamiltonian is smooth.
The relation between finite and infinite system nonanalyticities is illustrated
by means of a simple classical spin-like model which is exactly solvable for
both, finite and infinite system sizes, showing a phase transition in the
latter case. The microcanonical entropy is found to have exactly one
nonanalytic point in the interior of its domain. For all finite system sizes,
this point is located at the same fixed energy value $\epsilon_{c}^{finite}$,
jumping discontinuously to a different value $\epsilon_{c}^{infinite}$ in the
thermodynamic limit. Remarkably, $\epsilon_{c}^{finite}$ equals the average
potential energy of the infinite system at the phase transition point. The
result, supplemented with results on nonanalyticities of the microcanonical
entropy for other models, indicates that care is required when trying to infer
infinite system properties from finite system nonanalyticities.
