The Zero Temperature Phase Diagram of the Kitaev Model

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 $3\times 3$ 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.