Dimensional phase transition in superconductors with short coherence length

We found a novel dimensional transition in the vortex lattice of a finite-sized superconductor. The low-field dependence (with field applied parallel to the film plane) of the magnetization exhibits two maxima, which signal the transition from one to two dimensions. In one dimension the vortices line up along the film, and with increasing field their arrangement changes into a two-dimensional array due to the competition between vortex-surface and vortex-vortex repulsion. Agreement is found with no adjustable parameter calculations using a priori known surface-barrier and vortex-repulsion effects.