Interactions and disorder in quantum dots: instabilities and phase transitions

Using a fermionic renormalization group approach, we analyze a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by random matrix theory, we find that interactions can induce phase transitions (or crossovers for finite systems) to regimes where fluctuations and collective effects dominate at low energies. Implications for experiments and numerical work on quantum dots are discussed.