# Critical Two-Point Function for Long-Range Models with Power-Law Couplings: The Marginal Case for $${d\ge d_{\rm c}}$$d≥dc

@article{Chen2018CriticalTF,
title={Critical Two-Point Function for Long-Range Models with Power-Law Couplings: The Marginal Case for \$\$\{d\ge d\_\{\rm c\}\}\$\$d≥dc},
author={Lung-Chi Chen and Akira Sakai},
journal={Communications in Mathematical Physics},
year={2018},
pages={1-30}
}
• Published 21 August 2018
• Mathematics, Physics
• Communications in Mathematical Physics
Consider the long-range models on $${\mathbb{Z}^d}$$Zd of random walk, self-avoiding walk, percolation and the Ising model, whose translation-invariant 1-step distribution/coupling coefficient decays as $${|x|^{-d-\alpha}}$$|x|-d-α for some $${\alpha > 0}$$α>0 . In the previous work (Chen and Sakai in Ann Probab 43:639–681, 2015), we have shown in a unified fashion for all $${\alpha\ne2}$$α≠2 that, assuming a bound on the “derivative” of the $${n}$$n -step distribution (the compound-zeta…
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