Crossover from three- to two-dimensional behavior of the vortex energies in layeredXYmodels for high-Tcsuperconductors

We use Monte Carlo simulations of a layered XY model to study phase fluctuations in high-${\mathit{T}}_{\mathit{c}}$ superconductors. A vortex-antivortex interaction dominated by a term linear in the vortex separation is found in the low-temperature regime. This is in agreement with a zero-temperature variational calculation. At temperature just above the two-dimensional (2D) vortex-unbinding temperature, the linear term vanishes and an ordinary 2D vortex behavior is found. This explains the finding that high-${\mathit{T}}_{\mathit{c}}$ superconductors show 2D properties in the vortex fluctuations responsible for the resistivity transition close to the critical temperature.