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Direct determination of the collective pinning radius in high temperature superconductors

We study finite-size effects at the onset of the irreversible magnetic behaviour of micron-sized Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals by using silicon micro-oscillators. We find an irreversibility line appearing well below the thermodynamic Bragg-glass melting line at a magnetic field which increases both with increasing the sample radius and with decreasing the temperature. We show that this size-dependent irreversibility line can be identified with the crossover between the Larkin and the random manifold regimes of the vortex lattice transverse roughness. Our method allows to determine the three-dimensional weak collective pinning Larkin radius in a {\it direct way}.