  Along with experiments, numerical simulations are key to gaining insight into
the underlying mechanisms governing domain wall motion in thin ferromagnetic
systems. However, a direct comparison between numerical simulation of model
systems and experimental results still represents a great challenge. Here, we
present a tuned Ginzburg-Landau model to quantitatively study the dynamics of
domain walls in quasi two-dimensional ferromagnetic systems with perpendicular
magnetic anisotropy. This model incorporates material and experimental
parameters and the micromagnetic prescription for thermal fluctuations,
allowing us to perform material-specific simulations and at the same time
recover universal features. We show that our model quantitatively reproduces
previous experimental velocity-field data in the archetypal perpendicular
magnetic anisotropy Pt/Co/Pt ultra-thin films in the three dynamical regimes of
domain wall motion (creep, depinning and flow). In addition, we present a
statistical analysis of the domain wall width parameter, showing that our model
can provide detailed nano-scale information while retaining the complex
behavior of a statistical disordered model.
