  We consider the two-layer Heisenberg antiferromagnet near a zero temperature
quantum phase transition from a disordered dimer phase to a collinear Neel
state. At approaching the transition point the spin-wave gap vanishes as
$\Delta \propto (J_\perp-J_{\perp c})^{\nu}$. To account for strong
correlations between the S=1 elementary excitations we apply the Brueckner
diagram approach which gives the critical index $\nu\approx 0.5$. We
demonstrate also that the linearized 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, give $\nu\approx
0.67$. This value reasonably agrees 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.
