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We investigate the dimensionally induced phase transition from the normal tothe Bose-Einstein-condensed phase for a weakly interacting Bose gas in anoptical lattice. To this end we make use of the Hartree-Fock-Bogoliubov-Popovtheory, where we include numerically exact hopping energies and effectiveinteraction strengths. At first we determine the critical chemical potential,where we find a much better agreement with recent experimental data than a pureHartree-Fock treatment. This finding is in agreement with the dominant role ofquantum fluctuations in lower dimensions, as they are explicitly included inour theory. Furthermore, we determine for the 1D-3D-transition the power-lawexponent of the critical temperature for two different non-interacting Bose gasmodels yielding the same value of 1/2, which indicates that they belong to thesame universality class. For the weakly interacting Bose gas we find for bothmodels that this exponent is robust with respect to finite interactionstrengths.

Dimensionally Induced Phase Transition of the Weakly Interacting Ultracold Bose Gas