We use nonperturbative renormalization group techniques to calculate the momentum dependence of thermal fluctuations of graphene, based on a self-consistent calculation of the momentum-dependent elastic constants of a tethered membrane. We find a sharp crossover from the perturbative to the anomalous regime, in excellent agreement with Monte Carlo results for the out-of-plane fluctuations of graphene, and give an accurate value for the crossover scale. Our work strongly supports the notion that graphene is well described as a tethered membrane. Ripples emerge naturally from our analysis.

We investigate the role of the effective nucleon-nucleon interaction in the description of giant dipole resonances in hot nuclei. For this purpose we calculate the response function of hot nuclear matter to a small isovector external perturbation using various effective Skyrme interactions. We find that for Skyrme forces with an effective mass close to unity an undamped zero sound mode occurs at zero temperature. This mode gives rise in finite nuclei (calculated via the Steinwedel-Jenssen model) to a resonance whose energy agrees with the observed value. We find that zero sound disappears at a temperature of a few MeV, leaving only a broad peak in the dipole strength.For Skyrme forces with a small value of the effective mass (0.4-0.5), there is no zero sound at zero temperature but only a weak peak located too high in energy. The strength distribution in this case is nearly independent of temperature and shows small collective effects. The relevance of these results for the saturation of photon multiplicities observed in recent experiments is pointed out.

We investigate the response function of hot nuclear matter to a small isovector external field using a simplified Skyrme interaction reproducing the value of the symmetry energy coefficient. We consider values of the momentum transfer corresponding to the dipole oscillation in heavy nuclei. We find that while at zero temperature the particle hole interaction is almost repulsive enough to have a sharp (zero sound type) collective oscillation, such is no longer the case at temperatures of a few MeV. As a result a broadening of the dipole resonance occurs, leading to its quasi disappearence by the time the temperature reaches 5 MeV. The sensivity of the temperature evolution of the width when modifying the residual interaction strength is also examined.

We investigate the properties of crystalline phantom membranes, at the crumpling transition and in the flat phase, using a nonperturbative renormalization group approach. We avoid a derivative expansion of the effective average action and instead analyze the full momentum dependence of the elastic coupling functions. This leads to a more accurate determination of the critical exponents and further yields the full momentum dependence of the correlation functions of the in-plane and out-of-plane fluctuation. The flow equations are solved numerically for D = 2 dimensional membranes embedded in a d = 3 dimensional space. Within our approach we find a crumpling transition of second order which is characterized by an anomalous exponent η{c} ≈ 0.63(8) and the thermal exponent ν ≈ 0.69. Near the crumpling transition the order parameter of the flat phase vanishes with a critical exponent β ≈ 0.22. The flat phase anomalous dimension is η{f} ≈ 0.85 and the Poisson's ratio inside the flat phase is found to be σ{f} ≈ -1/3. At the crumpling transition we find a much larger negative value of the Poisson's ratio σ{c} ≈ -0.71(5). We discuss further in detail the different regimes of the momentum dependent fluctuations, both in the flat phase and in the vicinity of the crumpling transition, and extract the crossover momentum scales which separate them.