<p>The main focus of this thesis lies on the critical properties of twodimensional (2D) superconductors in zero magnetic field. Simulations based on variants of the 2D XY model are shown to give characteristic features close to the phase transition which agree qualitatively with experimental data. Thus, it is concluded that these common characteristic features are caused by two-dimensional vortices.</p><p>The thesis consists of an introductory part and five separate publications. In the introductory part of the thesis the basic results of the Ginzburg-Landau model, which gives a phenomenological description of superconductors, are described. In 2D systems, the superconductive phase transition in the absence of a magnetic field is governed by the unbinding of thermally created vortices and is called the Kosterlitz-Thouless (KT) phase transition. An introduction to this kind of transition is given. The important features of the current-voltage (IV) characteristics and the nonlinear conductivity, which can be used to study the KT transition, are discussed. The scaling analysis procedure, a powerful tool for the analysis of the properties of a system in the vicinity of phase transition, is reviewed. A scaling form for the nonlinear dc conductivity, which takes into account finite-size e ects, is discussed.</p><p>The static 2D XY model, which is usually used to describe superfluids, superconducting films as well as the high-Tc superconductors with high anisotropy, is introduced. Three different types of dynamic models, namely resistively shunted junction, relaxational, and Monte Carlo dynamics are superimposed on the 2D XY model for the evaluation of the dynamic properties. TheVillain model and a modifiedXY model using a p-type interaction potential exhibit different densities of the thermally created vortices. Since the dominant characteristic physical features close to the KT transition are associated with vortex pair fluctuations these two models are investigated.</p><p>The introductory part closes with a short introduction to each of the five published articles.</p>

The main focus of this thesis lies on the critical properties of twodimensional (2D) superconductors in zero magnetic field. Simulations based on variants of the 2D XY model are shown to give characteristic features close to the phase transition which agree qualitatively with experimental data. Thus, it is concluded that these common characteristic features are caused by two-dimensional vortices. The thesis consists of an introductory part and five separate publications. In the introductory part of the thesis the basic results of the Ginzburg-Landau model, which gives a phenomenological description of superconductors, are described. In 2D systems, the superconductive phase transition in the absence of a magnetic field is governed by the unbinding of thermally created vortices and is called the Kosterlitz-Thouless (KT) phase transition. An introduction to this kind of transition is given. The important features of the current-voltage (IV) characteristics and the nonlinear conductivity, which can be used to study the KT transition, are discussed. The scaling analysis procedure, a powerful tool for the analysis of the properties of a system in the vicinity of phase transition, is reviewed. A scaling form for the nonlinear dc conductivity, which takes into account finite-size e ects, is discussed. The static 2D XY model, which is usually used to describe superfluids, superconducting films as well as the high-Tc superconductors with high anisotropy, is introduced. Three different types of dynamic models, namely resistively shunted junction, relaxational, and Monte Carlo dynamics are superimposed on the 2D XY model for the evaluation of the dynamic properties. TheVillain model and a modifiedXY model using a p-type interaction potential exhibit different densities of the thermally created vortices. Since the dominant characteristic physical features close to the KT transition are associated with vortex pair fluctuations these two models are investigated. The introductory part closes with a short introduction to each of the five published articles.