Disorder relevance and the continuum random field Ising model

Since its introduction by Lenz in 1920, the Ising model has been one of the most studied statistical mechanics models. It has been particularly central in the theory of critical phenomena since Peierls famously proved that it undergoes a phase transition in dimension at least 2. We discuss the long considered question of whether this picture is changed by the addition of disorder acting as a small random external field and whether the model admits a disordered continuum limit.