  Within the micro-canonical ensemble phase transitions of first order can be
identified without invoking the thermodynamic limit. We show for the liquid-gas
transition of sodium, potassium, and iron at normal pressure that the
transition temperature, the latent heat as well as the interface surface
tension approach for some 1000 atoms the experimental bulk values. No excursion
to the thermodynamic limit is neccessary. It is often easier to identify the
transition in mesoscopic systems than in the infinite system. It is shown that
the microcanonical T(E) contains important information about the transition
which becomes suppressed in the canonical ensemble. The implications for our
understanding of phase transitions in general are discussed. For these finite
metallic systems it is essential to allow for a fragmentation of the system.
Our result demonstrates further that microcanonical Metropolis Monte Carlo
sampling (MMMC) is well suited to establish the link between the fragmentation
phase transition in small systems like nuclei and atomic clusters and the
liquid-gas transition of infinite matter.
