Spin-wave gap critical index for the quantum two-layer heisenberg antiferromagnet at T=0

The two-layer Heisenberg antiferromagnet exhibits a zero temperature quantu m phase transition from a disordered dimer phase to a collinear Neel phase, with long range order in the ground state. The spin-wave gap vanishes as D elta proportional to (J(perpendicular to) - J(perpendicular to c))(nu) appr oaching the transition point. To account for strong correlations, the S = 1 elementary excitations triplets are described as a dilute Bose gas with in finite on-site repulsion. We apply the Brueckner diagram approach which giv es the critical index nu approximate to 0.5. We demonstrate also that the l inearised 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 approximate to 0.67. This v alue agrees reasonably with that of the nonlinear O(3) sigma model. Our app roach demonstrates that for other quantum spin models the critical index ca n be different from that in the nonlinear sigma model. We discuss the condi tions for this to occur.