The Kibble–Zurek mechanism describes the nonadiabatic dynamics resulting from driving a high-symmetry (i.e. disordered) phase λ λ ≪ ≪ 0 to a broken-symmetry (i.e. ordered) phase at λ λ ≫ ≫ 0 . If the control parameter varies linearly in time, λ λ ( t ) = v t , equating the time to the critical point to the relaxation time, we obtain the freeze out time t ¯ ¯ , t ¯ ¯ = [ λ λ ( t ¯ ¯ ) ] − − z ν ν ⇒ ⇒ t ¯ ¯ ∼ ∼ v − − z ν ν / ( 1 + z ν ν ) . This time scale is often referred to as the freeze-out time. It is the intersection point of the blue and the red curve in the figure. The distance to the transition is on one hand side the time to reach the transition as function of cooling rate (red curve) and for linear cooling rates at the same time the difference of the control parameter to the critical point (blue curve). As the system approaches the critical point, it freezes as a result of the critical slowing down and falls out of equilibrium. Adiabaticity is lost around − − t ¯ ¯ . Adiabaticity is restored in the broken-symmetry phase after + t ¯ ¯ . The correlation length at this time provides a length scale for coherent domains, ξ ξ ¯ ¯ ≡ ≡ ξ ξ [ λ λ ( t ¯ ¯ ) ] ∼ ∼ v − − ν ν / ( 1 + z ν ν ) . The size of the domains in the broken-symmetry phase is set by ξ ξ ¯ ¯ . The density of defects immediately follows if d is the dimension of the system, using ρ ρ ∼ ∼ ξ ξ ¯ ¯ − − d .