What is it about?
Analytical solutions for the order-parameter dynamics in second-order phase transitions reveal why the long-standing theory of defect formation works so universally and so well. They also point to new experimental observables for the Kibble–Zurek mechanism (KZM), bridging the long-standing gap between the “freeze-out” conjecture—invoked to justify KZM scaling—and the order-parameter dynamics that can be measured in experiments.
Featured Image
Photo by Logan Voss on Unsplash
Why is it important?
The Kibble–Zurek mechanism (KZM) has long been celebrated for successfully predicting the density of topological defects that remain after a system undergoes a second-order phase transition. Yet the reason behind its striking universality has remained a mystery. In a new study published in PNAS, researchers from Los Alamos National Laboratory provide the first dynamical explanation for why the KZM works so well. Their analysis shows that the temporal evolution of the order parameter plays a crucial role in determining the formation of defects, and that this evolution can be solved analytically in key examples of KZM such as the Landau–Ginzburg and Gross–Pitaevskii models of phase transitions. Near the critical point of a second-order phase transition, systems experience critical slowing down: they become too sluggish to follow rapid changes in their potential energy landscape. As a result, there is a “frozen” period during which the system’s order parameter: It is still buffeted by noise, but it stops responding to the changes in the potential, locking in the correlation length. That scale sets the density of defects. The analytical solution for the order parameter evolution reveals this process, linking the dynamics of the order parameter to the central “feezeout” insight of the KZM. These findings suggest new experimental strategies—such as tracking the evolution of the order parameter during a second-order phase transition through measurements of magnetization, polarization, or Bose–Einstein condensate density—that can provide unprecedented insight into the dynamics of symmetry-breaking responsible for the KZM. This bridges a long-standing gap between the “freezeout” conjecture invoked to justify KZM scaling and the order parameter dynamics, suggesting experiments to reveal details of the symmetry breaking process while offering new insight into the fundamental principles underlying the KZM.
Perspectives
The Kibble–Zurek mechanism (KZM) is often discussed primarily in terms of the power-law scaling of topological-defect density with the quench rate. This study goes further by examining the nonequilibrium order-parameter dynamics during the phase transition itself. It demonstrates how experimentally measurable order-parameter dynamics can be directly connected to the “freeze-out” conjecture that forms the basis of the KZM.
Fumika Suzuki
Los Alamos National Laboratory
Read the Original
This page is a summary of: Deconstructing dynamics of symmetry breaking, Proceedings of the National Academy of Sciences, November 2025, Proceedings of the National Academy of Sciences,
DOI: 10.1073/pnas.2523903122.
You can read the full text:
Contributors
The following have contributed to this page
