  The magnetization ripple is a microstructure formed in thin ferromagnetic
films. It can be described by minimizers of a nonconvex energy functional
leading to a nonlocal and nonlinear elliptic SPDE in two dimensions driven by
white noise, which is singular. We address the universal character of the
magnetization ripple using variational methods based on $\Gamma$-convergence.
Due to the infinite energy of the system, the (random) energy functional has to
be renormalized. Using the topology of $\Gamma$-convergence, we give a sense to
the law of the renormalized functional that is independent of the way white
noise is approximated. More precisely, this universality holds in the class of
(not necessarily Gaussian) approximations to white noise satisfying the
spectral gap inequality, which allows us to obtain sharp stochastic estimates.
As a corollary, we obtain the existence of minimizers with optimal regularity.
