  We study the phase diagram of the superconducting vortex system in layered
high-temperature superconductors in the presence of a magnetic field
perpendicular to the layers and of random atomic scale point pinning centers.
We consider the highly anisotropic limit where the pancake vortices on
different layer are coupled only by their electromagnetic interaction. The free
energy of the vortex system is then represented as a Ramakrishnan-Yussouff free
energy functional of the time averaged vortex density. We numerically minimize
this functional and examine the properties of the resulting phases. We find
that, in the temperature ($T$) -- pinning strength ($s$) plane at constant
magnetic induction, the equilibrium phase at low $T$ and $s$ is a Bragg glass.
As one increases $s$ or $T$ a first order phase transition occurs to another
phase that we characterize as a pinned vortex liquid. The weakly pinned vortex
liquid obtained for high $T$ and small $s$ smoothly crosses over to the
strongly pinned vortex liquid as $T$ is decreased or $s$ increased -- we do not
find evidence for the existence, in thermodynamic equilibrium, of a distinct
vortex glass phase in the range of pinning parameters considered here. %cdr We
present results for the density correlation functions, the density and defect
distributions, and the local field distribution accessible via $\mu$SR
experiments. These results are compared with those of existing theoretical,
numerical and experimental studies.
