Kibble-Zurek mechanism and infinitely slow annealing through critical points

2010/01/05 by Giulio Biroli, Leticia F. Cugliandolo, Alberto Sicilia · 3 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Annealing (glass) #Condensed matter physics #Critical phenomena #Phase transition #Physics #Quantum many-body systems #Quantum mechanics #Statistical physics #Symmetry breaking #Theoretical and Computational Physics #Theoretical physics #Thermodynamics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.81.050101

5 pages, 4 figs

arxiv created 2010/01/05 · openalex publication_date 2010/05/06 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Defect formation and critical dynamics in the early Universe
• Phase-transition dynamics in the lab and the universe
• Cooling dynamics of pure and random Ising chains
• Vortex String Formation in a 3D U(1) Temperature Quench
• Theory of dynamic critical phenomena
• Nonappearance of Vortices in Fast Mechanical Expansions of Liquid4Hethrough the Lambda Transition
• Slow cooling of an Ising ferromagnet
• Domain growth morphology in curvature-driven two-dimensional coarsening
• Topology of cosmic domains and strings
• Quenched Kosterlitz-Thouless Superfluid Transitions

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