Summary: The two-layer Heisenberg antiferromagnet exhibits a zero temperature quantum phase transition from a disordered dimer phase to a collinear Néel phase, with long range order in the ground state. The spin-wave gap vanishes as \(\sigma \propto (J \perp - J \perp c) \nu\) approaching the transition point. To account for strong correlations, the \(S = 1\) elementary excitations triplets are described as a dilute Bose gas with infinite on-site repulsion. We apply the Brueckner diagram approach which gives the critical index \(\nu \asymp \circ .5\). We demonstrate also that the linearised in density Brueckner equations give the mean field result \(\nu = 1\). Finally, an expansion of the Brueckner equations in powers of the density, combined with the scaling hypothesis, gives \(\nu \asymp \circ .67\). This value agrees reasonably with that of the nonlinear \(O(3)\) \(\sigma\)-model. Our approach demonstrates that for other quantum spin models the critical index can be different from that in the nonlinear \(\sigma\)-model. We discuss the conditions for this to occur.