Classification of Phase Transitions for an Ideal Bose Gas in a d-Dimensional Quartic Potential

Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number N of particles trapped in a d-dimensional quartic potential. We find that the presence and nature of phase transition depend on the dimensionality of the quartic potential. Proposing three different definitions of transition temperature, we discuss either N or d dependence of transition temperature for the ideal Bose condensate in the d-dimensional quartic potential.