Finite-volume effects in O(N)-models

The investigation of QCD phases is currently a much discussed topic in particle physics. In the context of this discussion the knowledge about the nature of chiral phase transition is significant. A powerful tool for this purpose are lattice simulations. They are, however, still carried out at quark masses far from the chiral limit and in small volumes, which could strongly influence the critical behavior. Since continuous phase transitions are controlled by the long range fluctuations only the dimensionality and symmetries dictate the universal behavior near the critical point. Therefore, more simple systems from the same universality class can be used to analyze QCD at chiral phase transition. We investigate 3-dimensional O(2)- and O(4)-models in finite volumes using non-perturbative Renormalization Group methods. We provide scaling functions in infinite and finite volume that are universal for O(2)- and O(4)-universality classes in d=3 dimensions and applicable to the chiral phase transition. We also investigate the effects of the finite volume on the critical behavior and determine the finite-size scaling region for both models in order to provide a tool, which assists in analysis of lattice QCD data.