Is There Kibble-Zurek Scaling of Topological Defects in First-Order Phase Transitions?

Kibble-Zurek scaling is the scaling of the density of topological defects formed via the Kibble-Zurek mechanism with respect to the rate at which a system is cooled across a continuous phase transition. Recently, the density of the topological defects formed via the Kibble-Zurek mechanism was estimated for a system cooled through a first-order phase transition rather than conventional continuous transitions. Here we address the problem of whether such defects generated across a first-order phase transition exhibit Kibble-Zurek scaling similar to the case in continuous phase transitions. We show that any possible Kibble-Zurek scaling for the topological defects can only be a very rough approximation due to an intrinsic field responsible for the scaling. However, complete universal scaling for other properties does exist.