Fig. 3: Numerically computed \({\log }_{10}\left(L/\xi \right)\) as a function of \({\log }_{10}(| \alpha | \gamma t)\) for 2ζ = 0.0001, and the linear fitting.

In the numerical simulation, space and time are discretized by step sizes 0.5ξ and 0.03(∣α∣γ)⁻¹. Data points are selected within \({\log }_{10}(L/\xi )\in (1,1.2)\). The results are statistical averages over ten independent simulations. a The 3D U(1) symmetric case. b The 3D U(1) breaking case with β/∣α∣ = 0.1. Both (a) and (b) are simulated in a L_x × L_y × L_z grid with L_z/ξ = 60, L_x/ξ = L_y/ξ = 1280. c, d The 2D case with the Z₂ term β/∣α∣ being (c) 0.001 and (d) 0.1. The phase distribution of a topological defect is sketched in the inset of (d) with the same colorbar as Fig. 2b, c. Both (c) and (d) are simulated in a L_y × L_z grid with L_z/ξ = 120, L_y/ξ = 38,400.