Rare Events Govern Defect Formation under Weak Symmetry Breaking
Abstract
Crossing a continuous phase transition out of equilibrium typically generates topological defects whose density obeys a universal power-law scaling predicted by the Kibble-Zurek mechanism. Recent numerical studies have revealed systematic deviations from this scaling in the presence of weak explicit symmetry breaking, manifested as an additional exponential suppression of defect formation. However, the origin of this correction and a general theoretical framework to describe it have remained elusive. Here, using large-deviation theory, we show that defect formation under weak symmetry breaking is controlled by rare fluctuations that drive local regions into the disfavored symmetry-broken state. Within mean-field theory, this mechanism yields a closed-form expression for the defect density in arbitrary dimensions, valid in the weak-field and weak-noise limits. These theoretical predictions are verified through direct simulations of stochastic Ginzburg-Landau models in one and two spatial dimensions.
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BibTeX
@misc{liu2026rare,
title = {{Rare Events Govern Defect Formation under Weak Symmetry Breaking}},
author = {Jiang Liu and Peng Yang and Matteo Baggioli},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.27835},
eprint = {2606.27835},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.27835},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rare Events Govern Defect Formation under Weak Symmetry Breaking
AU - Jiang Liu
AU - Peng Yang
AU - Matteo Baggioli
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2606.27835
UR - https://arxiv.org/abs/2606.27835
AB - Crossing a continuous phase transition out of equilibrium typically generates topological defects whose density obeys a universal power-law scaling predicted by the Kibble-Zurek mechanism. Recent numerical studies have revealed systematic deviations from this scaling in the presence of weak explicit symmetry breaking, manifested as an additional exponential suppression of defect formation. However, the origin of this correction and a general theoretical framework to describe it have remained elusive. Here, using large-deviation theory, we show that defect formation under weak symmetry breaking is controlled by rare fluctuations that drive local regions into the disfavored symmetry-broken state. Within mean-field theory, this mechanism yields a closed-form expression for the defect density in arbitrary dimensions, valid in the weak-field and weak-noise limits. These theoretical predictions are verified through direct simulations of stochastic Ginzburg-Landau models in one and two spatial dimensions.
ER -