Statistical mechanics of vortex system in a thin superconducting film in cycle approximation II. Finite thickness and vortex bending

The interaction between two point vortices in a superconducting film of finite thickness is obtained. The result differs from well known Pearl's one by the new effective penetration depth $\Lambda '=\lambda \mathop {\rm cth}\nolimits {\frac {d}{2 \lambda }}$. The partition sum is calculated in cycle approximation and the vortex bending fluctuations are taking into account in the frame of an approach analogous to the quasiclassical approximation. The influence of both these correction terms on the Kosterlitz-Thouless transition and the resistance curve is discussed.