  We study the ultrametric structure of phase space of one-dimensional Ising
spin glasses with random power-law interaction in an external random field.
Although in zero field the model in both the mean-field and non-mean-field
universality classes shows an ultrametric signature [Phys. Rev. Lett. 102,
037207 (2009)], when a field is applied ultrametricity seems only present in
the mean-field regime. The results for the non-mean field case in an external
field agree with data for spin glasses studied within the Migdal-Kadanoff
approximation. Our results therefore suggest that the spin-glass state might be
fragile to external fields below the upper critical dimension.
