期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 337, 期 2, 页码 817-877出版社
SPRINGER
DOI: 10.1007/s00220-015-2352-6
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资金
- NSERC of Canada
- National Science Foundation [DMS-1128155]
- University of British Columbia
- IAM at the University of Bonn
- Department of Mathematics and Statistics at McGill University
- Institute for Advanced Study at Princeton
- Institut Henri Poincare
- Mathematical Institute of Leiden University
- Eurandom
We prove that the susceptibility of the continuous-time weakly self-avoiding walk on , in the critical dimension d = 4, has a logarithmic correction to mean-field scaling behaviour as the critical point is approached, with exponent for the logarithm. The susceptibility has been well understood previously for dimensions d a parts per thousand yen 5 using the lace expansion, but the lace expansion does not apply when d = 4. The proof begins by rewriting the walk two-point function as the two-point function of a supersymmetric field theory. The field theory is then analysed via a rigorous renormalisation group method developed in a companion series of papers. By providing a setting where the methods of the companion papers are applied together, the proof also serves as an example of how to assemble the various ingredients of the general renormalisation group method in a coordinated manner.
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