Ja n 19 97 Various series expansions for the bilayer S = 1 2 Heisenberg antiferromagnet

Various series expansions have been developed for the two-layer, S = 1 2 , square lattice Heisenberg antiferromagnet. High temperature expansions are used to calculate the temperature dependence of the susceptibility and specific heat. At T = 0, Ising expansions are used to study the properties of the Néel-ordered phase, while dimer expansions are used to calculate the ground-state properties and excitation spectra of the magnetically disordered phase. The antiferromagnetic order-disorder transition point is determined to be (J 2 /J 1) c = 2.537(5). Quantities computed include the staggered magne-tization, the susceptibility, the triplet spin-wave excitation spectra, the spin-wave velocity, and the spin-wave stiffness. We also estimates that the ratio of the intra-and inter-layer exchange constants to be J 2 /J 1 ≃ 0.07 for cuprate superconductor YBa 2 Cu 3 O 6.2 .