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In contrast to the canonical ensemble where thermodynamic functions aresmooth for all finite system sizes, the microcanonical entropy can shownonanalytic points also for finite systems, even if the Hamiltonian is smooth.The relation between finite and infinite system nonanalyticities is illustratedby means of a simple classical spin-like model which is exactly solvable forboth, finite and infinite system sizes, showing a phase transition in thelatter case. The microcanonical entropy is found to have exactly onenonanalytic 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 thethermodynamic limit. Remarkably, $\epsilon_{c}^{finite}$ equals the averagepotential energy of the infinite system at the phase transition point. Theresult, supplemented with results on nonanalyticities of the microcanonicalentropy for other models, indicates that care is required when trying to inferinfinite system properties from finite system nonanalyticities.Comment: 4 pages, 1 figur

Nonanalyticities of Entropy Functions of Finite and Infinite Systems