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Angular-dependent magnetic torque measurements performed near the criticaltemperature on single crystals of HgBa_{2}CuO_{4+y}, La_{2-x}Sr{x}CuO_{4}, andYBa_{2}Cu_{3}O_{6.93} are scaled, following the 3D XY model, in order todetermine the scaling function dG^{\pm}(z)/dz which describes the universalcritical properties near T_{c}. A systematic shift of the scaling function withincreasing effective mass anisotropy \gamma = (m_{ab}*/m_{c}*)^{1/2} isobserved, which may be understood in terms of a 3D-2D crossover. Furtherevidence for a 3D-2D crossover is found from temperature-dependent torquemeasurements carried out in different magnetic fields at different fieldorientations \delta, which show a quasi 2D "crossing region'' (M*,T*). Theoccurrence of this "crossing phenomenon'' is explained in a phenomenologicalway from the weak z dependence of the scaling function around a value z = z*.The "crossing'' temperature T* is found to be angular-dependent. Torquemeasurements above T_{c} reveal that fluctuations are strongly enhanced in theunderdoped regime where the anisotropy is large, whereas they are lessimportant in the overdoped regime.Comment: 9 pages, 10 figures, submitted to PR

Torque magnetometry on single-crystal high-temperature superconductors near the critical temperature: A scaling approach