  We show that the zero temperature phase diagram of the vortex free sector of
the Kitaev model is in one to one correspondence with that of the classical
dimer model on the same lattice. We find that the model generically has three
distinct phases. On a honeycomb lattice with a $3\times3$ fundamental domain
all three phases are accessible. As the couplings are varied there are two
distinct transitions. The new transition is one to a gapped phase that opens up
in the interior of the $B$ phase.
