On quasi twodimensional XY magnetism and superconductivity of the second kind

Abstract

The role of interplanar fluctuations associated with « parallel » vortex loops is considered in the two coupled problems of XY magnetism and superconductivity of the second kind, in a quasitwodimensional situation. Using an admittedly simplified criterion, it is argued that, for weak interplanar couplings, the critical 3d temperature is related to the multiplication of such loops ; it should be below the Kosterlitz and Thouless temperature where « normal » vortex loops, piercing the planes, would multiply in independent planes