  Kitaev's compass model on the honeycomb lattice realizes a spin liquid whose
emergent excitations are dispersive Majorana fermions and static Z_2 gauge
fluxes. We discuss the proper selection of physical states for finite-size
simulations in the Majorana representation, based on a recent paper by
Pedrocchi, Chesi, and Loss [Phys. Rev. B 84, 165414 (2011)]. Certain physical
observables acquire large finite-size effects, in particular if the ground
state is not fermion-free, which we prove to generally apply to the system in
the gapless phase and with periodic boundary conditions. To illustrate our
findings, we compute the static and dynamic spin susceptibilities for
finite-size systems. Specifically, we consider random-bond disorder (which
preserves the solubility of the model), calculate the distribution of local
flux gaps, and extract the NMR lineshape. We also predict a transition to a
random-flux state with increasing disorder.
