Rare Events Govern Defect Formation under Weak Symmetry Breaking
arXiv:2606.27835
The paper explains how rare fluctuations, analyzed via large‑deviation theory, control the formation of topological defects when a continuous phase transition occurs under weak explicit symmetry breaking, providing a universal formula for defect density that matches simulations.
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. 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.
v2: extended analysis and references added