  We report an experimental determination of the phase boundary between a
quantum paramagnetic state and the proposed spin Bose-Einstein condensate of
triplons in the spin gap compound BaCuSi2O6. The ordering temperature is
related to the proximity to a quantum critical point at the lower critical
magnetic field H_c1 = 23.52 +/- 0.03T by a power law parameterized by critical
exponent nu. We obtain an experimental estimate of nu = 0.63 +/- 0.03 which is
in good agreement with the mean field prediction of nu = 2/3 for the 3D XY
model, used to describe the Bose condensation of a 3D dilute interacting Bose
gas.
