  On the basis of a macroscopic ground state population it was argued recently
that Bose-Einstein condensation should occur in a one-dimensional harmonic
potential. We examine this situation by drawing analogies to Bosons in a
two-dimensional box, where the thermodynamic limit is well-defined. We show
that in both systems although the ground state populations show sharp onsets at
the critical temperature, the behaviour of the specific heat is analytic, which
proves the absence of a phase transition in these systems.
