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Correct Bounds on the Ising Lace-Expansion Coefficients
| Title: | Correct Bounds on the Ising Lace-Expansion Coefficients |
| Authors: | Sakai, Akira Browse this author →KAKEN DB |
| Issue Date: | Jun-2022 |
| Publisher: | Springer |
| Journal Title: | Communications in mathematical physics |
| Volume: | 392 |
| Issue: | 3 |
| Start Page: | 783 |
| End Page: | 823 |
| Publisher DOI: | 10.1007/s00220-022-04354-5 |
| Abstract: | The lace expansion for the Ising two-point function was successfully derived in (Sakai in Commun Math Phys 272:283-344, 2007, Proposition 1.1). It is an identity that involves an alternating series of lace-expansion coefficients. In the same paper, we claimed that the expansion coefficients obey certain diagrammatic bounds which imply faster x-space decay (as the two-point function cubed) above the critical dimension d(c) (= 4 for finite-variance models) if the spin-spin coupling is ferromagnetic, translation-invariant, summable and symmetric with respect to the underlying lattice symmetries. However, we recently found a flaw in the proof of (Sakai in Commun Math Phys 272:283-344, 2007, Lemma 4.2), a key lemma to the aforementioned diagrammatic bounds. In this paper, we no longer use the problematic (Sakai 2007, Lemma 4.2), and prove new diagrammatic bounds on the expansion coefficients that are slightly more complicated than those in (Sakai 2007, Proposition 4.1) but nonetheless obey the same fast decay above the critical dimension d(c). Consequently, the lace-expansion results for the Ising and phi(4) models in the literature are all saved. The proof is based on the random-current representation and its source-switching technique of Griffiths, Hurst and Sherman, combined with a double expansion: a lace expansion for the lace-expansion coefficients. |
| Rights: | This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00220-022-04354-5 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/90112 |
| 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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