Topological Defect Statistics in a Weakly First-Order Phase Transition
Abstract
The celebrated Kibble-Zurek mechanism (KZM) characterizes the nonequilibrium dynamics of second-order phase transitions and predicts universal scaling of the average number of defects with the quench time. However, the KZM is not directly applicable to first-order phase transitions, where defect formation is instead governed by nucleation processes. Here, using a Ginzburg-Landau model, we investigate the defect-number statistics in a weakly first-order phase transition. We show that the resulting statistics contain signatures of both Kibble-Zurek dynamics and nucleation, revealing the interplay between these two defect-formation mechanisms. In particular, we find that the defect-number distribution evolves from approximately Gaussian to nearly Poissonian across the crossover from the KZM regime to nucleation-dominated defect formation. While the first two cumulants are well described by a simple additive estimate of the KZM and nucleation contributions, the third cumulant exhibits a plateau and an enhancement beyond this estimate, providing a sensitive probe of the interplay between the two defect-formation mechanisms.
Related
- First-principles-based search for emergent topological spin textures in transition-metal dichalcogenide monolayers
- Random field approximation and local counting statistics for the weakly interacting thermal Bose gas
- Universal Defect Statistics in Reverse Quenches
- Finite-size scaling theory of Rényi thermal entropy for second-order, first-order, and weakly first-order quantum phase transitions
- Topological Pseudo-Goldstone Modes from Weakly Broken Dipole Conservation
BibTeX
@misc{rottman2026topological,
title = {{Topological Defect Statistics in a Weakly First-Order Phase Transition}},
author = {Antonin Rottman and Leonard Logarić and Fumika Suzuki and Adolfo del Campo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02022},
eprint = {2611.02022},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02022},
}
RIS
TY - UNPB
TI - Topological Defect Statistics in a Weakly First-Order Phase Transition
AU - Antonin Rottman
AU - Leonard Logarić
AU - Fumika Suzuki
AU - Adolfo del Campo
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02022
UR - https://arxiv.org/abs/2611.02022
AB - The celebrated Kibble-Zurek mechanism (KZM) characterizes the nonequilibrium dynamics of second-order phase transitions and predicts universal scaling of the average number of defects with the quench time. However, the KZM is not directly applicable to first-order phase transitions, where defect formation is instead governed by nucleation processes. Here, using a Ginzburg-Landau model, we investigate the defect-number statistics in a weakly first-order phase transition. We show that the resulting statistics contain signatures of both Kibble-Zurek dynamics and nucleation, revealing the interplay between these two defect-formation mechanisms. In particular, we find that the defect-number distribution evolves from approximately Gaussian to nearly Poissonian across the crossover from the KZM regime to nucleation-dominated defect formation. While the first two cumulants are well described by a simple additive estimate of the KZM and nucleation contributions, the third cumulant exhibits a plateau and an enhancement beyond this estimate, providing a sensitive probe of the interplay between the two defect-formation mechanisms.
ER -