Metastability and Phase Transitions

This lecture delves into the concept of metastability and phase transitions, exploring the relationship between energy barriers, probability of barrier crossing, and the dynamics of systems in finite dimensions. The instructor illustrates how metastability manifests in the Ising model, discussing the implications of transitioning between different energy minima. The lecture also touches on the complexity of algorithmic problems in finite dimensions and the challenges posed by nucleation in systems with finite sizes. Additionally, the lecture connects the concepts of metastability to first-order phase transitions, showcasing the common image of the liquid-gas transition and the spinodal decomposition. The discussion extends to the behavior of systems in finite dimensions and the significance of spinodal lines in defining phase transitions.