Kibble-Zurek mechanism and infinitely slow annealing through critical points

TL;DR

This paper revisits the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering during infinitely slow annealing across a second order phase transition, focusing on defect formation and scaling.

Contribution

It extends the Kibble-Zurek mechanism by analyzing defect formation during slow annealing and identifying its limitations in phase ordering systems.

Findings

Derived the dependence of defect density on cooling rate.

Predicted the scaling of correlation length during slow annealing.

Identified limitations of the Kibble-Zurek mechanism in certain regimes.

Abstract

We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second order phase transition. We elucidate the time and cooling rate dependence of the typical growing length and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.