The unidentified X-ray source RX J0720.4-3125 is a candidate isolated neutron star showing evidence for pulsed emission with an 8.39 s period and a spectrum consistent with a blackbody at kT=80 eV (Haberl et al. 1996, 1997). We show that this source is most likely an old isolated neutron star accreting from surrounding media. We then argue that unless it was born with a long spin period (P_i >~ 0.5 seconds) and weak field (B_i <~ 10^10 G), the magnetic field on this star must have decayed. With B_i ~ 10^12 G, we find decay timescales >~ 10^7 yrs for power law decay or >~ 10^8 yrs for exponential decay. A measured period derivative Pdot <~ 10^{-16} s s^{-1} would be consistent with an old accreting isolated neutron star. Both power law and exponential decay models can give a Pdot ~ 10^{-16} s s^{-1}, though a Pdot substantially less than this would be indicative of exponential field decay.

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