A two-dimensional superconducting array with applied external currents is studied in an analytical way. We obtain a Fokker-Planck equation from the Langevin equation ruling the time evolution of the system, and introduce a pseudo-Hamiltonian to describe the stationary solution of the Fokker-Planck equation. The pseudo-Hamiltonian is transformed into a Coulomb-gas Hamiltonian, which, via the renormalization-group technique, leads to the Kosterlitz-Thouless transition.

• Received 22 August 1991

DOI:https://doi.org/10.1103/PhysRevB.44.10411