  Building on recent neutron and NMR experiments, we investigate the
field-induced exotic criticality observed in the frustrated spin-1/2 dimer
compound BaCuSi2O6 using a frustrated model with two types of bilayers. A
semiclassical treatment of the effective hard-core boson model shows that
perfect inter-layer frustration leads to a 2D-like critical exponent phi=1
without logarithmic corrections and to a 3D low temperature phase with
different but non vanishing triplet populations in both types of bilayers.
These results further suggest a simple phenomenology in terms of a
field-dependent transverse coupling in the context of which we reproduce the
entire field-temperature phase diagram with Quantum Monte Carlo simulations.
