Metastability under stochastic dynamics (Q2485796)

The paper is intended as a tutorial introduction to rigorous (mathematical physics) results on metastable states for physical systems, whose behavior is persistent against rapid changes of their phase-transition driving parameters. The system may stay unusually long in its initial phase (metastable state), and only due to random fluctuations can be ultimately pushed to a new phase. Rigorous results to metastability were obtained for the Ising model, continuouos models (fluid), van der Waals gas, general interacting particle systems with emphasis on droplet formation. Recently, a mathematical background for metastability has been established, in terms of large deviation theory [\textit{E. Olivieri} and \textit{M. E. Vares}, ``Large deviations and metastabillity'' (2004; Zbl 1075.60002)]. The main focus of the paper is the formation of so-called critical droplets, their geometry and time of their appearance. Special attention is paid to Ising spins subject to the Glauber spin-flip dynamics and lattice particles subject to the Kawasaki hopping dynamics.