Magnetic fluctuations in 2D metals close to the Stoner instability

We consider the effect of potential disorder on magnetic properties of a two-dimensional metallic system (with conductance $g\gg 1$) when 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 form local spin droplets which are local regions with non zero spin density. Using a non-local version of the optimal fluctuation method we find analytically the probability distribution and the typical spin of a local spin droplet (LSD). In particular, we show that both the probability to form a LSD and its typical spin are independent of the size of the droplet (within the exponential accuracy). The LSDs manifest themselves in temperature dependence of observable quantities. We show, that below certain cross-over temperature the paramagnetic susceptibility acquires the Curie-like temperature dependence, while the dephasing time (extracted from magneto-resistance measurements) saturates.