Topological defects formed during a phase transition quench: n ~ τ_Q^(−ν/(1+νz))
Quench time τ_Q20
Correlation exp ν0.63
Dynamics exp z2.0
Grid size40
The Kibble-Zurek mechanism predicts that cooling through a phase transition at rate τ_Q⁻¹ freezes out order at the Zurek time t̂ ~ τ_Q^(νz/(1+νz)), producing defect density n ~ ξ̂^(−d) ~ τ_Q^(−ν/(1+νz)).
Left: 2D XY model spins during a quench — vortices (red) and antivortices (blue) are topological defects. Right: scaling law from sweeping τ_Q.
For 3D Ising (ν≈0.63, z≈2): exponent = ν/(1+νz) ≈ 0.24.