We study the phase diagram at T=0 of the antiferromagnetic Heisenberg model
on the triangular lattice with spatially-anisotropic interactions. For values
of the anisotropy very close to J_alpha/J_beta=0.50, conventional spin wave
theory predicts that quantum fluctuations melt the classical structures, for
S=1/2. For the regime J_beta<J_alpha, it is shown that the incommensurate
spiral phases survive until J_beta/J_alpha=0.27, leaving a wide region where
the ground state is disordered. The existence of such nonmagnetic states
suggests the possibility of spin liquid behavior for intermediate values of the
anisotropy.Comment: Revised version, 4 pages, Latex (twocolumn), 4 figures as eps files.
To appear in PR