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This functional is a close relative of the scalar Ginzburg-Landau functional $J(u) = \\int |\\nabla u|^2 + W(u)$, where $W(u) = (1-u^2)^2/2$ is a standard double-well potential. According to a famous conjecture of De Giorgi, global critical points of $J$ that are bounded and monotone in one direction have level sets that are hyperplanes, at least up to dimension $8$. 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