The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
  Results from exact diagonalization show that the spin-polarized Coulomb ground state at nu=5/2 is adiabatically connected with the Moore-Read wave function for systems with up to Nel = 16 electrons on the surface of a sphere. Varying the Haldane pseudopotentials v1 and v3, keeping all others at their value for Coulomb interaction, energy gap and (v1,v3)-dependent ground state overlap with the Moore-Read state form two ridges whose peak positions and extent in the (v1,v3)-plane essentially coincide. Thus, the physics of the Coulomb ground state at nu=5/2 is indeed captured by the Moore-Read state and that non-Abelian statistics can be expected under experimental conditions. Such adiabatic connection is not observed at nu=1/2, unless the width of the interface wave function and/or Landau level mixing effects are sufficiently large. Varying the width, an excitation gap is found for all system sizes Nel \le 18 studied. However, its system size dependence casts doubt on the existence of a Moore-Read-phase at nu=1/2 in the thermodynamic limit. 
M. Storni, R. H. Morf and S. Das Sarma