  The evolution of magnetic field in isolated neutron stars is one of the most
important ingredients in the attempt to build a unified description of these
objects. A prediction of field evolution models is the existence of an
equilibrium configuration, in which the Hall cascade vanishes. Recent
calculations have explored the field structure in this stage, called the Hall
attractor. We use X-ray data of near-by, cooling neutron stars to probe this
prediction, as these sources are surmised to be close to or at Hall attractor
phase. We show that the source RX J1856.5-3754 might be closer to the attractor
than other sources of its class. Our modelling indicates that the properties of
surface thermal emission, assuming that the star is in the Hall attractor, are
in contradiction with the spectral data of RX J1856.5-3754.
