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We show that the spatial dimensionality of the quantum critical pointassociated with Bose--Einstein condensation at T=0 is reduced when theunderlying lattice comprises a set of layers coupled by a frustratinginteraction. Our theoretical predictions for the critical temperature as afunction of the chemical potential correspond very well with recentmeasurements in BaCuSi$_{2}$O$_{6}$ [S. E. Sebastian \textit{et al}, Nature\textbf{411}, 617 (2006)].Comment: 5 pages, 2 figure

Geometric Frustration and Dimensional Reduction at a Quantum Critical Point