Zero-temperature spin-wave spectrum of the critical two-layerS=1/2 antiferromagnet

Series expansions about the interlayer dimer limit are calculated to eighth order in the intralayer coupling for the T=0 antiferromagnetic susceptibility and elementary excitation spectrum of the two-layer, S=1/2, square lattice Heisenberg antiferromagnet. Extrapolations of the susceptibility and the gap series yield an estimate of the critical interlayer/intralayer coupling ratio J₂/J₁=2.54±{}0.02, in agreement with several previous numerical calculations. The spin-wave velocity at criticality is determined by an analysis of the excitation spectrum series: the result, {}c/J₁a=1.89±{}0.02, is very precise and consistent with other estimates based on numerical calculations at finite temperature. The critical spin-wave dispersion at general wave vectors is shown to deviate significantly from a uniformly renormalized mean-field spectrum. {} 1996 The American Physical Society.