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Title: Non-Gaussian scaling limit of the critical 3D Ising model
Plain: In four or more dimensions the critical Ising model looks like a free (Gaussian) field at large scales. In 3D it should not, and this difference is unproven.
Precise: Prove that every subsequential scaling limit of the critical spin field on $Z^{3}$ is non-Gaussian, for example that the rescaled fourth Ursell function does not vanish, and that $\eta > 0$ strictly (the infrared bound gives only $\eta \ge 0$). Answer: a proof.
Settled by: A proof of a nonvanishing four-point Ursell function in the 3D scaling limit.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: open
Status note: Gaussianity is proven for $d \ge 5$ (Aizenman; Frohlich, 1982) and $d = 4$ (Aizenman and Duminil-Copin, 2021).
Posed since: (empty)