  We study quantum antiferromagnets on two-dimensional bipartite lattices. We
focus on local variations in the properties of the ordered phase which arise
due to the presence of inequivalent sites or bonds in the lattice structure,
using linear spin wave theory and quantum Monte Carlo methods. Our primary
finding is that sites with a high coordination tend to have a low ordered
moment, at odds with the simple intuition of high coordination favoring more
robust Neel ordering. The lattices considered are the dice lattice, which is
dual to the kagome, the CaVO lattice, an Archimedean lattice with two
inequivalent bonds, and the crown lattice, a tiling of squares and rhombi with
a greater variety of local environments. We present results for the onsite
magnetizations and local bond expectation values for the spin-1/2 Heisenberg
model on these lattices, and discuss the exactly soluble model of a Heisenberg
star, which provides a simple analytical framework for understanding our
lattice studies.
