We study the spin-half Heisenberg models on an anisotropic two-dimensional
lattice which interpolates between the square-lattice at one end, a set of
decoupled spin-chains on the other end, and the triangular-lattice Heisenberg
model in between. By series expansions around two different dimer ground states
and around various commensurate and incommensurate magnetically ordered states,
we establish the phase diagram for this model of a frustrated antiferromagnet.
We find a particularly rich phase diagram due to the interplay of magnetic
frustration, quantum fluctuations and varying dimensionality. There is a large
region of the usual 2-sublattice Ne\'el phase, a 3-sublattice phase for the
triangular-lattice model, a region of incommensurate magnetic order around the
triangular-lattice model, and regions in parameter space where there is no
magnetic order. We find that the incommensurate ordering wavevector is in
general altered from its classical value by quantum fluctuations. The regime of
weakly coupled chains is particularly interesting and appears to be nearly
critical.Comment: RevTeX, 15 figure