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The vortex phase transition in La(1.44)Nd(0.4)Sr(0.16)CuO(4) epitaxial films with different thicknesses under a compressive strain were studied systematically by measuring the current-voltage (IV) characteristics in magnetic fields perpendicular to the CuO(2) planes. For a strongly compressed thin film, in which the static stripe order is destroyed, the IV curves show a good three-dimensional (3D) vortex glass (VG) scaling collapse in various magnetic fields, indicating a 3D VG phase transition. By applying the standard scaling procedure to the data of a strain-released thick film with static stripe order, neither a 3D nor a quasi-2D VG model works well. Further investigation shows that, in order to achieve a good scaling collapse, the Kosterlitz-Thouless correlation length should be used for the isothermals above T(g). The scaling of isothermals below T(g) can also be optimized if the VG correlation length and adjusted static critical exponent nu are used with D = 2 only, indicating that a quasi-2D VG phase might exist. Our findings reveal that the nature of the vortex phase transition is completely altered in the presence of the stripe order.

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