|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
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)
|
Submitter: 坂井 哲
|
