  We study a simple model of symmetry-enriched topological order obtained by
decorating a toric code model with lower-dimensional symmetry-protected
topological states. We show that the symmetry fractionalization in this model
can be characterized by string order parameters, and that these signatures are
robust under the effects of external fields and interactions, up to the phase
transition point. This extends the recent proposal of [New Journal of Physics
21, 113016 (2019)] beyond the setting of fixed-point tensor network states, and
solidifies string order parameters as a useful tool to characterize and detect
symmetry fractionalization. In addition to this, we observe how the
condensation of an anyon that fractionalizes a symmetry forces that symmetry to
spontaneously break, and we give a proof of this in the framework of projected
entangled pair states. This phenomenon leads to a notable change in the phase
diagram of the toric code in parallel magnetic fields.
