Phase Transition, Longitudinal Spin Fluctuations and Scaling in a Two-Layer Antiferromagnet

We consider a two-layer Heisenberg antiferromagnet which can be either in the N\'{e}el-ordered or in the disordered phase at $T=0$, depending on the ratio of the intra- and interlayer exchange constants. We reduce the problem to an interacting Bose-gas and study the sublattice magnetization and the transverse susceptibility in the ordered phase, and the spectrum of quasiparticle excitations in both phases. We compare the results with the spin-wave theory and argue that the longitudinal spin fluctuations, which are not included in the spin-wave description, are small at vanishing coupling between the layers, but increase as the system approaches the transition point. We also compute the uniform susceptibility at the critical point to order $O(T^2)$, and show that the corrections to scaling are numerically small, and the linear behavior of $\chi_u$ extends to high temperatures. This is consistent with the results of the recent Monte-Carlo simulations by Sandvik and Scalapino.