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Conditions for the Existence and Stability of the Continuous Attractor in the Classical XY Model with an Associative-Memory-Type Interaction
http://hdl.handle.net/10935/4565
http://hdl.handle.net/10935/4565e936ec21-82b0-47df-8e25-e57c0552e4ce
| 名前 / ファイル | ライセンス | アクション |
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AA00704814V86p034001-1-034001-26.pdf
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| アイテムタイプ | default_学術雑誌論文 / Journal Article(1) | |||||||||||||||||
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| タイトル | ||||||||||||||||||
| タイトル | Conditions for the Existence and Stability of the Continuous Attractor in the Classical XY Model with an Associative-Memory-Type Interaction | |||||||||||||||||
| 言語 | en | |||||||||||||||||
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| 言語 | eng | |||||||||||||||||
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| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||||||||
| 資源タイプ | journal article | |||||||||||||||||
| 著者 |
吉田,梨紗
× 吉田,梨紗
× 木本,智幸
× 上江洌,達也 |
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| 抄録 | ||||||||||||||||||
| 内容記述タイプ | Abstract | |||||||||||||||||
| 内容記述 | We analyze the structure of attractors in the classical XY model with an associative-memory-type interaction by the statistical mechanical method. Previously, it was found that when patterns are uncorrelated, points on a path connecting two memory patterns in the space of the order parameters are solutions of the saddle point equations (SPEs) in the case that p O(1) irrespective of N and N ≫ 1, where p and N are the numbers of patterns and spins, respectively. This state is called the continuous attractor (CA). In this paper, we clarify the conditions for the existence and stability of the CA with and without the correlation a (0 〓 a < 1) between any two patterns in the case that N ≫ 1 and the self-averaging property holds. We find that the CA exists for any p 〓 2 when a = 0, but it exists only for p = 2 when 0 < a < 1 and for p = 3 when a < 1/3. For p = 2 and 3, and for a < 1, we analyze the SPEs and find all solutions and study their stabilities. We perform Markov chain Monte Carlo simulations and compare numerical and theoretical results. We find that for a finite system of size N and for a = 0, owing to the breakdown of the self-averaging property, the CA ceases to exist at a finite value of p. We define the critical value of pc until which the CA exists and numerically study the system size N dependence of pc. We find that the numerical results are consistent with the theoretical results obtained by taking into account the breakdown of the self-averaging property. Furthermore, for a > 0, we numerically study the case that patterns are subject to external noise and find that pc increases as the noise amplitude increases. | |||||||||||||||||
| 言語 | en | |||||||||||||||||
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| 内容記述タイプ | Other | |||||||||||||||||
| 内容記述 | 本文データの著作権は一般社団法人日本物理学会(The Physical Society of Japan)が保有する。 | |||||||||||||||||
| 言語 | ja | |||||||||||||||||
| 書誌情報 |
en : Journal of the Physical Society of Japan 巻 86, 号 3, p. 034001-1-034001-26, 発行日 2017-02-02 |
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| 出版者 | ||||||||||||||||||
| 出版者 | The Physical Society of Japan 一般社団法人 日本物理学会 | |||||||||||||||||
| 言語 | ja | |||||||||||||||||
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| 収録物識別子タイプ | PISSN | |||||||||||||||||
| 収録物識別子 | 0031-9015 | |||||||||||||||||
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| 識別子タイプ | NCID | |||||||||||||||||
| 関連識別子 | AA00704814 | |||||||||||||||||
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| 関連タイプ | isVersionOf | |||||||||||||||||
| 識別子タイプ | DOI | |||||||||||||||||
| 関連識別子 | https://doi.org/10.7566/JPSJ.86.034001 | |||||||||||||||||
| 関連名称 | 10.7566/JPSJ.86.034001 | |||||||||||||||||
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| 出版タイプ | AM | |||||||||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||||||||||
