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The effect of columnar pins on the flux-lines melting transition inhigh-temperature superconductors is studied using Path Integral Monte Carlosimulations. We highlight the similarities and differences in the effects ofcolumnar disorder on the melting transition in YBa$_2$Cu$_3$O$_{7-\delta}$(YBCO) and the highly anisotropic Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO) atmagnetic fields such that the mean separation between flux-lines is smallerthan the penetration length. For pure systems, a first order transition from aflux-line solid to a liquid phase is seen as the temperature is increased. Whenadding columnar defects to the system, the transition temperature is notaffected in both materials as long as the strength of an individual columnardefect (expressed as a flux-line defect interaction) is less than a certainthreshold for a given density of randomly distributed columnar pins. Thisthreshold strength is lower for YBCO than for BSCCO. For higher strengths thetransition line is shifted for both materials towards higher temperatures, andthe sharp jump in energy, characteristic of a first order transition, gives wayto a smoother and gradual rise of the energy, characteristic of a second ordertransition. Also, when columnar defects are present, the vortex solid phase isreplaced by a pinned Bose glass phase and this is manifested by a markeddecrease in translational order and orientational order as measured by theappropriate structure factors. For BSCCO, we report an unusual rise of thetranslational order and the hexatic order just before the melting transition.No such rise is observed in YBCO.Comment: 32 pages, 13 figures, revte

Effects of columnar disorder on flux-lattice melting in high-temperature superconductors