Classical Kitaev model in a magnetic field

We study the classical version of Kitaev's honeycomb model in the presence of a magnetic field. For an anti-ferromagnetic Kitaev coupling a classical spin liquid phase persists over a large window of field strength, independent of field direction. We characterize this phase using analytic arguments, a coarse-grained theory and via Monte Carlo simulations, finding the Coulomb correlations present at zero-field are immediately destroyed when the field is applied. We further probe the nature of this phase via the introduction of vacancies. Over a wide field range we find removing a site leaves the magnetization unchanged, the liquid exactly compensating the missing spin. Finally, we speculate on implications for the quantum model in the semi-classical limit.