Quantum triviality refers to the phenomenon that an interacting lattice model converges to a free field in the scaling limit. This has been established for Ising and Phi^4 models, at or above their upper critical dimensions. We describe a simple spin model from uniform spanning forests in $/Z^d$ whose critical dimension is 4 and prove that the scaling limit is the bi-Laplacian Gaussian field for $d/ge 4$. At dimension 4,there is a logarithmic correction for the spin-spin correlation and the bi-Laplacian Gaussian field is a log correlated field. Based on joint works with Greg Lawler and Xin Sun.

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