Classification of phase transitions in small systems

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the compl ex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the righ t critical indices. We apply this classification scheme to Bose-Einstein co ndensates in a harmonic trap as an example of a higher order phase transiti on in a finite system and to small Ar clusters.