First-order versus Kosterlitz-Thouless transition in a class of modifiedXYmodels

We analyze the possibility of understanding the nonuniversal jump of the superconducting density in thin films of high-${\mathit{T}}_{\mathit{c}}$ superconductors in terms of XY models with a modified interaction V(θ) (quadratic for small ‖θ‖ and flat for ‖θ‖>${\mathrm{\theta }}_{\mathit{c}}$). We introduce a method to map such models on a Coulomb-gas model with logarithmic interaction and show that the unusual properties observed in numerical simulations do not imply that the transition is first order, but can be understood within the context of a vortex-unbinding Kosterlitz-Thouless transition. These results suggest that a nonuniversal jump of the superconducting density might require something other than a modification of the interaction potential V(θ).