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 3x3 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.