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Gaussian deconvolution and the lace expansion for spread-out models (2310.07640v2)
Published 11 Oct 2023 in math.PR, math-ph, and math.MP
Abstract: We present a new proof of $|x|{-(d-2)}$ decay of critical two-point functions for spread-out statistical mechanical models on $\mathbb{Z}d$ above the upper critical dimension, based on the lace expansion and assuming appropriate diagrammatic estimates. Applications include spread-out models of the Ising model and self-avoiding walk in dimensions $d>4$, and spread-out percolation for $d>6$. The proof is based on an extension of the new Gaussian deconvolution theorem we obtained in a paper. It provides a technically simpler and conceptually more transparent approach than the method of Hara, van der Hofstad and Slade (2003).
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