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Critical two-point functions for long-range statistical-mechanical models in high dimensions
Title: | Critical two-point functions for long-range statistical-mechanical models in high dimensions |
Authors: | Chen, Lung-Chi Browse this author | Sakai, Akira Browse this author →KAKEN DB |
Issue Date: | Mar-2015 |
Publisher: | Institute of Mathematical Statistics |
Journal Title: | The Annals of Probability |
Volume: | 43 |
Issue: | 2 |
Start Page: | 639 |
End Page: | 681 |
Publisher DOI: | 10.1214/13-AOP843 |
Abstract: | We consider long-range self-avoiding walk, percolation and the Ising model on Zd that are defined by power-law decaying pair potentials of the form D(x)≍|x|−d−α with α>0. The upper-critical dimension dc is 2(α∧2) for self-avoiding walk and the Ising model, and 3(α∧2) for percolation. Let α≠2 and assume certain heat-kernel bounds on the n-step distribution of the underlying random walk. We prove that, for d>dc (and the spread-out parameter sufficiently large), the critical two-point function Gpc(x) for each model is asymptotically C|x|α∧2−d, where the constant C∈(0,∞) is expressed in terms of the model-dependent lace-expansion coefficients and exhibits crossover between α<2 and α>2. We also provide a class of random walks that satisfy those heat-kernel bounds. |
Type: | article |
URI: | http://hdl.handle.net/2115/57803 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 坂井 哲
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