The X-ray spectral energy distribution of isolated neutron stars shows no evidence of atmospheric spectral features due to atomic transitions. This unexpected lack of spectral lines, together with the systematic optical excess (with respect to the X-ray best fit extrapolation) observed in several objects, is one of the current paradigms in the theoretical understanding of neutron stars. We investigate the thermal emission from neutron star surfaces in which the cohesive effects of a strong magnetic field have produced the condensation of the atmosphere and the external layers. This may happen for sufficiently cool (T :5 101) atmospheres with moderately intense magnetic fields (about 10(13) G for Fe at,face shows no remarkable spectral mospheres). The thermal emission from such a bare sur features. In addition, since the thermal conductivity is very different in the perpendicular and parallel directions to the magnetic field lines, the presence of the magnetic field is expected to produce a highly anisotropic temperature distribution at the surface of the star, depending on the magnetic field geometry. The observed flux from this objects looks very similar to a blackbody spectrum, but depressed by a nearly constant factor at all energies. More interestingly, if one takes into account the effect of the motion of ions in a crude approximation, combined with the anisotropic thermal distribution, it results in an apparent optical excess. Both facts seem to indicate that some isolated neutron stars are old, cold magnetars.