We study a model for the depinning and driven steady state phases of a solid
tuned across a polymorphic phase transition between ground states of triangular
and square symmetry. These include pinned states which may have dominantly
triangular or square correlations, a plastically flowing liquid-like phase, a
moving phase with hexatic correlations, flowing triangular and square states
and a dynamic coexistence regime characterized by the complex interconversion
of locally square and triangular regions. We locate these phases in a dynamical
phase diagram. We demonstrate that the apparent power-law orientational
correlations we obtain in our moving hexatic phase arise from circularly
averaging an orientational correlation function with qualitatively different
behaviour in the longitudinal (drive) and transverse directions. The
intermediate coexistence regime exhibits several novel properties, including
substantial enhancement in the current noise, an unusual power-law spectrum of
current fluctuations and striking metastability effects. This noise arises from
the fluctuations of the interface separating locally square and triangular
ordered regions. We demonstrate the breakdown of effective ``shaking
temperature'' treatments in the coexistence regime by showing that such shaking
temperatures are non-monotonic functions of the drive in this regime. Finally
we discuss the relevance of these simulations to the anomalous behaviour seen
in the peak effect regime of vortex lines in the disordered mixed phase of
type-II superconductors. We propose that this anomalous behavior is directly
linked to the behavior exhibited in our simulations in the dynamical
coexistence regime, thus suggesting a possible solution to the problem of the
origin of peak effect anomalies.Comment: 22 pages, double column, higher quality figures available from
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