  We simulate the dc magnetic response of the diluted dipolar-coupled Ising
magnet LiHo\(_{0.045}\)Y\(_{0.955}\)F\(_4\) in a transverse field, using exact
diagonalization of a two-spin Hamiltonian averaged over nearest-neighbour
configurations. The pairwise model, incorporating hyperfine interactions,
accounts for the observed drop-off in the longitudinal (c-axis) susceptibility
with increasing transverse field; with the inclusion of a small tilt in the
transverse field, it also accounts for the behavior of the off-diagonal
magnetic susceptibility. The hyperfine interactions do not appear to lead to
qualitative changes in the pair susecptibilities, although they do renormalize
the crossover fields between different regimes. Comparison with experiment
indicates that antiferromagnetic correlations are more important than
anticipated based on simple pair statistics and our first-principles
calculations of the pair response. This means that larger clusters will be
needed for a full description of the reduction in the diagonal response at
small transverse fields.
