  We present a phase-coherent timing solution for RX J0420.0-5022, the coolest
(kT=45 eV) and fastest-spinning (P=3.45 s) of the seven so-called isolated
neutron stars (INSs). Using 14 observations with the XMM-Newton spacecraft in
2010-2011, we were able to measure a spin-down rate nudot=(-2.3+/-0.2)e-15 Hz/s
(Pdot=(2.8+/-0.3)e-14 s/s), from which we infer a dipolar magnetic field of
1.0e13 G. With reasonable confidence we were able to extend the timing solution
back to archival XMM-Newton from 2002 and 2003, giving the same solution but
with considerably more precision. This gives RX J0420 the lowest dipole
magnetic field of the INSs. Our spectroscopy does not confirm the broad
absorption feature at 0.3 keV hinted at in earlier observations, although
difficulties in background subtraction near that energy make conclusions
difficult. With this, all 6 of the INSs that have confirmed periodicities now
have constrained spin-downs from coherent solutions. The evidence that the INSs
are qualitatively different from rotation-powered pulsars now appears robust,
with the likely conclusion that their characteristic ages are systematically
older than their true ages, because their fields have decayed. The field decay
probably also causes them to be systematically hotter than pulsars of the same
(true) age.
