Microcanonical finite-size scaling of an ideal Bose gas in a box

We derive an exact recursive scheme to determine exactly the microcanonical partition function of a finite Bose system. Such a recursive approach is identical to that previously obtained within the context of counting statistics. Within the exact microcanonical ensemble, we study microcanonical finite-size scaling behaviors of condensate fraction and specific heat around the critical energy epsilon(c) for the finite ideal Bose system. We show that the microcanonical scaling functions governing the various critical behaviors are universal in the ideal Bose-Einstein condensates.