  We have numerically evaluated the current-current correlations for three-band
models of the CuO planes in high-T_c superconductors at hole doping x=1/8. The
results show no evidence for the orbital current patterns proposed by Varma. If
such patterns exist, the associated energy is estimated to be smaller than 5
meV per link even if epsilon_p-epsilon_d=0. Assuming that the three-band models
are adequate, quantum critical fluctuations of such patterns hence cannot be
responsible for phenomena occurring at significantly higher energies, such as
superconductivity or the anomalous properties of the pseudogap phase.
