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.
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