We study a frustrated 3D antiferromagnet of stacked $J_1 - J_2$ layers. The intermediate quantum spin liquid phase, present in the 2D case, narrows with increasing interlayer coupling and vanishes at a triple point. Beyond this there is a direct firs
t-order transition from N{ e}el to columnar order. Possible applications to real materials are discussed.
We use high-temperature series expansions to obtain thermodynamic properties of the quantum compass model, and to investigate the phase transition on the square and simple cubic lattices. On the square lattice we obtain evidence for a phase transitio
n, consistent with recent Monte Carlo results. On the simple cubic lattice the same procedure provides no sign of a transition, and we conjecture that there is no finite temperature transition in this case.
The energy spectrum of the two-magnon bound states in the Heisenberg-Ising antiferromagnet on the square lattice are calculated using series expansion methods. The results confirm an earlier spin-wave prediction of Oguchi and Ishikawa, that the bound
states vanish into the continuum before the isotropic Heisenberg limit is reached.
The S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the S=0 and S=1 channels, and antibound st
ates in the S=2 channel, is predicted by the triplet-wave theory, and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the Neel phase. The critical behaviour of the total and single-particle static transverse structure factors is also studied by series, and found to conform with theoretical expectations. The single-particle state dominates the structure factor at all couplings.
We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the $S = 1$ Heisenberg antiferromagnet with easy-axis or easy-plane single site anisotropy, on the square lattice. Series expansions are used, i
n each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared with spin-wave theory.
