  The aim of this article is to study the magnetic Ginzburg-Landau functional
with an oscillating pinning term. We consider here oscillations of the pinning
term that are much faster than the coherence length \(\varepsilon>0\) which is
also the inverse of the Ginzburg-Landau parameter. We study both the case of a
periodic potential and of a random stationary ergodic one. We prove that we can
reduce the study of the problem to the case where the pinning term is replaced
by its average, in the periodic case, and by its expectation with respect to
the random parameter in the random case. In order to do that we use a
decoupling of the energy due to Lassoued-Mironescu. This leads us to the study
of the convergence of a scalar positive minimizer of the Ginzburg-Landau energy
with pinning term and with homogeneous Neumann boundary conditions. We prove
uniform convergence of this minimizer towards the mean value of the pinning
term by using a blow-up argument and a Liouville type result for non-vanishing
entire solutions of the real Ginzburg-Landau/Allen-Cahn equation, due to
Farina.
