Seminarium Fizyki Materii Skondensowanej

After briefly introducing the nonperturbative functional renormalization group method, I explain two of its applications, for which the functional nature of the method is crucial. First of all I address the the question of how to calculate the probability distribution of the order parameter in critical systems. Since the first works of Wilson on the topic of the renormalization group it was understood that the quantities calculated within the RG should represent probabilities of observables. However no practical implementation for the calculation of probabilities was developed before our work. I will show how to calculate the distribution of critical order parameter and compare the results to the Monte Carlo calculations. Second application I will talk about is the analytical description of the approach to the lower critical dimension. This is the dimensionality where the transition at a finite temperature disappears due to entropy effects. These entropy effects are statistically rare and localized excitations such as kinks or instantons in systems with discrete symmetry or vertices and spin waves in the systems with continuous symmetry. The fundamental interest of this line of research is to understand how the localized excitations translate into long wavelength behavior within the functional RG approach.