  The self-consistency equations for the independent order parameters as well
as the free energy expression for the mean-field RVB model of the spin-1/2
Heisenberg Hamiltonian on the anisotropic triangular lattice is considered in
the quasi-one-dimensional approximation. The solutions of the self-consistency
equations in the zero-temperature limit are in fair agreement with the previous
numerical analysis of the same model by other authors. In particular, the
transition from the ungapped 1D-RVB state to the gapped 2D-RVB state occurs at
an arbitrarily weak transversal exchange ($J_{2}\rightarrow0)$ although the
amount of the gap is exponentially small:
$\frac{12J_{1}}{\pi}\exp(-\frac{2J_{1}}{J_{2}})$, where $J_{1}$ is the
longitudinal exchange parameter. The structural consequences of the formation
of the 2D-RVB state are formulated by extending the famous bond order
\emph{vs}. bond length relation known for polyenes (one-dimensional Hubbard
chains). Analytical estimates of this effect are given.
