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Monte Carlo simulations of layered BSCCO samples are used to investigate thebehavior of vortex matter at low fields, particularly in connection with thepossible occurrence of a Bragg glass (BrG) phase at low density of columnardefects, a phenomenon characterized by the prevalence of short-range overlong-range order. In this dislocation-free topological phase the translationalorder 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 planarstructure factor, the hexatic order parameter, and the Delaunay triangulationshows 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{highlyanisotropic} high-T${}_c$ superconductor. Most importantly, an analysis of the{low-temperature} 3D vortex-vortex correlation function in terms of thestructure factor, calculated via a saddle point approach and the use of thenumerical data as input, provides clear-cut evidence of {the} power law decayof the {divergent} Bragg peaks in the BrG phase, a fundamental feature that wasinequivocally verified only in isotropic compounds.

Monte Carlo Simulation of the Crossover from Bose Glass to Bragg Glass Phase in Layered BSCCO with Columnar Defects