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We present a detailed description of a classification scheme for phasetransitions in finite systems based on the distribution of Fisher zeros of thecanonical partition function in the complex temperature plane. We apply thisscheme to finite Bose-systems in power law traps within a semi-analyticapproach with a continuous one-particle density of states $\Omega(E)\simE^{d-1}$ for different values of $d$ and to a three dimensional harmonicallyconfined ideal Bose-gas with discrete energy levels. Our results indicate thatthe order of the Bose-Einstein condensation phase transition sensitivelydepends on the confining potential.

Classification of phase transitions of finite Bose-Einstein condensates in power-law traps by Fisher zeros