  Monte Carlo simulations of layered BSCCO samples are used to investigate the
behavior of vortex matter at low fields, particularly in connection with the
possible occurrence of a Bragg glass (BrG) phase at low density of columnar
defects, a phenomenon characterized by the prevalence of short-range over
long-range order. In this dislocation-free topological phase the translational
order correlation function displays a power law decay. For magnetic induction
$B=0.1$ kG the analysis of the data for the first Bragg peak of the planar
structure factor, the hexatic order parameter, and the Delaunay triangulation
shows that, as the density of columnar defects is lowered, a \textit{crossover}
(or transition) from Bose glass to BrG phase takes place in this \textit{highly
anisotropic} high-T${}_c$ superconductor. Most importantly, an analysis of the
{low-temperature} 3D vortex-vortex correlation function in terms of the
structure factor, calculated via a saddle point approach and the use of the
numerical data as input, provides clear-cut evidence of {the} power law decay
of the {divergent} Bragg peaks in the BrG phase, a fundamental feature that was
inequivocally verified only in isotropic compounds.
