  We study spin-half and spin-one Heisenberg models in the limit where one
dimensional (1-D) linear chains, with exchange constant J1, are weakly coupled
in an anisotropic triangular lattice geometry. Results are obtained by means of
linked-cluster series expansions at zero temperature around different
magnetically ordered phases. We study the non-colinear spiral phases that arise
classically in the model and the colinear antiferromagnet that has been
recently proposed for the spin-half model by Starykh and Balents using a
Renormalization Group approach. We find that such phases can be stabilized in
the spin-half model for arbitrarily small coupling between the chains. For
vanishing coupling between the chains the energy of each phase must approach
that of decoupled linear chains. With increasing inter-chain coupling, the
non-colinear phase appears to have a lower energy in our calculations. For the
spin-one chain, we find that there is a critical interchain coupling needed to
overcome the Haldane gap. When spin-one chains are coupled in an unfrustrated
manner, the critical coupling is very small (~0.01J1) and agrees well with
previous chain mean-field studies. When they are coupled in the frustrated
triangular-lattice geometry, the critical coupling required to develop magnetic
order is substantially larger (> 0.3J1). The colinear phase is not obtained for
the spin-one Heisenberg model.
