Phase transitions for an ideal Bose condensate trapped in a quartic potential

. Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number of particles confined in a three-dimensional quartic trap. We show that the phase transition of an ideal Bose gas in the three-dimensional quartic trap is of third order for finite particle numbers, quite different from the fact that the phase transition is of first order in the thermodynamic limit. We discuss the effects of finite particle numbers on the nature of the phase transitions, and determine the dependence of transition temperature on particle number.