The Scaling Limit of the ( ∇ + 1 ) -Model

In this article we study the scaling limit of the interface model on Z d where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free field. We discuss the appropriate spaces in which the convergence takes place. While in infinite volume the proof is based on Fourier analytic methods,infinitevolumewerelyonsomediscretePDEtechniquesinvolvingfinite-difference approximationofellipticboundaryvalueproblems

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