Critical exponent η_φ of the Lattice London Superconductor and vortex loops in the 3D XY model

The anomalous dimension of the lattice London superconductor is determined from finite size scaling of the susceptibility to be \eta_\phi = -0.79(1). Indirect determinations of \eta_\phi from properties of the vortex loops in the 3D XY model are also attempted, but it is found that the results are sensitive to details in the simulations related to vortex loop intersections. It is suggested that the same value of \eta_\phi can at most be obtained from vortex loop properties in the limit of low vortex density.