Dynamics of Phase Transitions: Between First and Second Order

Phase transitions are typically classified as either first-order or second-order. The formation of topological defects in second-order phase transitions is well described by the Kibble-Zurek mechanism, while nucleation theory addresses first-order phase transitions. However, certain systems, such as superconductors and liquid crystals, can exhibit “weakly first-order” phase transitions that do not fit into these established frameworks. In this presentation, I introduce a new theoretical approach that combines the Kibble-Zurek mechanism with nucleation theory to explain topological defect formation in weakly first-order phase transitions. Additionally, I will discuss nonlinear quantum phase transitions that exhibit behaviors similar to weakly first-order transitions, which can be related to experiments with ultra-cold Rydberg atoms.