Charge and vortex unbinding transitions in arrays of tunnel junctions

It has recently been suggested by Mooij et al. that electric charges on the islands of a network of tunnel junctions, if the nearest neighbor capacitances between the islands dominate, interact logarithmical, and as a consequence, a Kosterlitz-Thouless-Berezinskii transition can occur where charge-anticharge pairs dissociate. This paper discusses the effect of single electron and Cooper pair tunneling on this transition and discuss the competition between the charge unbinding transition and the more familiar vortex unbinding transition in superconducting networks