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タイトル: | Exact analytic expressions of real tensor eigenvalue distributions of Gaussian tensor model for small $N$ |
著者: | Sasakura, Naoki https://orcid.org/0000-0003-3668-1074 (unconfirmed) |
著者名の別形: | 笹倉, 直樹 |
キーワード: | Eigenvalue algorithm Monte Carlo methods Tensor formalism Fermion systems Boson systems Gaussian random field |
発行日: | 6-Jun-2023 |
出版者: | AIP Publishing |
誌名: | Journal of Mathematical Physics |
巻: | 64 |
号: | 6 |
論文番号: | 063501 |
抄録: | We obtain exact analytic expressions of real tensor eigenvalue/vector distributions of real symmetric order-three tensors with Gaussian distributions for $Nleq 8$. This is achieved by explicitly computing the partition function of a zero-dimensional boson-fermion system with four-interactions. The distributions are expressed by combinations of polynomial, exponential and error functions as results of feasible complicated bosonic integrals which appear after fermionic integrations. By extrapolating the expressions and also using a previous result, we guess a large-$N$ expression. The expressions are compared with Monte Carlo simulations, and precise and good agreement are obtained with the exact and the large-$N$ expressions, respectively. Understanding the feasibility of the integration is left for future study, which would provide a general-$N$ analytic formula. |
著作権等: | © 2023 Author(s). Published under an exclusive license by AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in (Naoki Sasakura; Exact analytic expressions of real tensor eigenvalue distributions of Gaussian tensor model for small N. J. Math. Phys. 6 June 2023; 64 (6): 063501.) and may be found at https://doi.org/10.1063/5.0133874. The full-text file will be made open to the public on JUNE 01 2024 in accordance with publisher's 'Terms and Conditions for Self-Archiving'. This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。 |
URI: | http://hdl.handle.net/2433/284868 |
DOI(出版社版): | 10.1063/5.0133874 |
出現コレクション: | 学術雑誌掲載論文等 |
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