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Center for Nonlinear Studies |
It is known since Peierls's pioneering work that the two-dimensional Ising model exhibits spontaneous magnetization at low temperatures---this is the meaning of the word "order" in the title. This phenomenon disappears when the model is modified to possess a continuous symmetry group (Mermin-Wagnertheorem) or when a random field term ("disorder") is added to its energy function (Imry-Ma instability). I will ask what happens when both modifications are applied and point at a surprising possibility that adding disorder to a continuous-symmetric system may order it again. I will present arguments in favor of such phenomenon and discuss its generalizations, including possible experimental consequences for ultracold atomic gases.