Disorder destroys long-range order below the lower critical dimension
The Imry-Ma argument (1975): in d dimensions, a domain of size L costs energy ~J*L^(d-1) (surface) but gains ~Delta*L^(d/2) (random field fluctuations). For d less than or equal to 2, the field term wins at large L, so ordered states are unstable and long-range order is destroyed. This was rigorously proved by Aizenman-Wehr (1989).