Magnetic fluctuations in two-dimensional metals close to the Stoner instability

We consider the effect of potential disorder on the magnetic properties of a two-dimensional metallic system (with conductance g much greater than1) w hen the interaction in the triplet channel is so strong that the system is close to the threshold of the Stoner instability. We show that under these conditions there is an exponentially small probability for the system to fo rm local spin droplets which are local regions with nonzero spin density. U sing a nonlocal version of the optimal fluctuation method we find analytica lly the probability distribution and the typical spin of a local spin dropl et (LSD). In particular, we show that both the probability to form a LSD an d its typical spin are independent of the size of the droplet (within the e xponential accuracy). The LSD's manifest themselves in the temperature depe ndence of the observable quantities. We show that below a certain crossover temperature the paramagnetic susceptibility acquires a Curie-like temperat ure dependence, while the dephasing time (extracted from magnetoresistance measurements) saturates.