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Applications of the Lace Expansion to Statistical-Mechanical Models
| Title: | Applications of the Lace Expansion to Statistical-Mechanical Models |
| Authors: | Sakai, Akira Browse this author →KAKEN DB |
| Keywords: | lace expansion | | phase transition | | Ising model | | self-avoiding walk | | percolation |
| Issue Date: | 2008 |
| Publisher: | Oxford University Press |
| Citation: | Analysis and stochastics of growth processes and interface models |
| Volume: | Chapter: 3.1 |
| Start Page: | 123 |
| End Page: | 147 |
| Publisher DOI: | 10.1093/acprof:oso/9780199239252.003.0006 |
| Abstract: | Synergetics is a common feature in interesting statistical-mechanical problems. One of the most important examples of synergetics is the emergence of a second-order phase transition and critical behaviour. It is rich and still far from fully understood. The reason why it is so difficult is due to the increase to infinity of the number of strongly correlated variables in the vicinity of the critical point. For example, the Ising model, which is a model for magnets, exhibits critical behaviour as the temperature comes closer to its critical value; the closer the temperature is to criticality, the more spin variables cooperate with each other to attain the global magnetization. In this regime, neither standard probability theory for independent random variables nor naive perturbation techniques work. The lace expansion, which is the topic of this article, is currently one of the few approaches to rigorous investigation of critical behaviour for various statistical-mechanical models. The chapter summarizes some of the most intriguing lace-expansion results for self-avoiding walk (SAW), percolation, and the Ising model. |
| Rights: | "Applications of the lace expansion to statistical-mechanical models" by "Analysis and Stochastics of Growth Processes and Interface Models" edited by Peter Mörters ...[et al.], 2008, reproduced by permission of Oxford University Press http://doi.org/10.1093/acprof:oso/9780199239252.003.0006 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/57861 |
| 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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