  We study the thermodynamic and structural properties of the superconducting
vortex system in high temperature layered superconductors, with magnetic field
normal to the layers, in the presence of a small concentration of strong random
point pinning defects via numerical minimization of a model free energy
functional in terms of the time-averaged local density of pancake vortices.
Working at constant magnetic induction and point pinning center concentration,
we find that the equilibrium phase at low temperature ($T$) and small pinning
strength ($s$) is a topologically ordered Bragg glass. As $T$ or $s$ is
increased, the Bragg glass undergoes a first order transition to a disordered
phase which we characterize as a ``vortex slush'' with polycrystalline
structure within the layers and interlayer correlations extending to about
twenty layers. This is in contrast with the pinned vortex liquid phase into
which the Bragg glass was found to melt, using the same methods, in the case of
a large concentration of weak pinning centers: that phase was amorphous with
very little interlayer correlation. The value of the second moment of the
random pinning potential at which the Bragg glass melts for a fixed temperature
is very different in the two systems. These results imply that the effects of
random point pinning can not be described only in terms of the second moment of
the pinning potential, and that some of the unresolved contradictions in the
literature concerning the nature of the low $T$ and high $s$ phase in this
system are likely to arise from differences in the nature of the pinning in
different samples, or from assumptions made about the pinning potential.
