  We study the effect of quenched disorder in square artificial spin ice by
means of numerical simulations. We introduce disorder in the length of magnetic
islands using two kinds of distributions: Gaussian and uniform. As the system
behavior depends on its geometrical parameters, we focus on studying it in the
proximity of the ice regime which is quite difficult to thermalize both in
experiments and simulations. We show how length disorder affect the
antiferromagnetic and (locally) ferromagnetic ordering, by inducing the system,
in the case of weak disorder, to intermediate or mix states. Moreover, in the
case of strong disorder, ferromagnetic plaquettes prevail regardless of whether
the mean length of the islands corresponds to an antiferromagnetic ordering.
