  Spin liquids occuring in 2D frustrated spin systems were initially assumed to
appear at strongest frustration, but evidence grows that they more likely
intervene at transitions between two different types of order. To identify if
this is more general, we here analyze a generalization of the spatially
anisotropic triangular lattice (SATL) with antiferromagnetic Heisenberg
interactions, the spatially \emph{completely} anisotropic triangular lattice
(SCATL). Using Takahashi's modified spin-wave theory, complemented by exact
diagonalizations, we find indications that indeed different kinds of order are
always separated by disordered phases. Our results further suggest that two
gapped non-magnetic phases, identified as distinct in the SATL, are actually
continuously connected via the additional anisotropy of the SCATL. Finally,
measurements on several materials found magnetic long-range order where
calculations on the SATL predict disordered behavior. Our results suggest a
simple explanation through the additional anisotropy of the SCATL, which
locates the corresponding parameter values in ordered phases. The studied model
might therefore not only yield fundamental insight into quantum disordered
phases, but should also be relevant for experiments on the quest for spin
liquids.
