Dual point description of mesoscopic superconductors

We present an analysis of the magnetic response of a mesoscopic superconductor, i.e., a superconducting sample of dimensions comparable to the coherence length and to the London penetration depth. Our approach is based on special properties of the two-dimensional Ginzburg-Landau equations, satisfied at the dual point (κ=1/√2). Closed expressions for the free energy and the magnetization of the superconductor are derived. A perturbative analysis in the vicinity of the dual point allows us to take into account vortex interactions, using a scaling result for the free energy. In order to characterize the vortex/current interactions, we study vortex configurations that are out of thermodynamical equilibrium. Our predictions agree with the results of recent experiments performed on mesoscopic aluminum disks.