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AA00704814V86p034001-1-034001-26.pdf1.18 MBAdobe PDF公開予定日: 2018-02-02
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
その他のタイトル: 
著者: Risa, Yoshida; Tomoyuki, Kimoto; Tatsuya, UEZU link image
著者(別表記) : 吉田, 梨紗; 木本, 智幸; 上江洌, 達也
著者読み: よしだ, りさ; きもと, ともゆき; うえづ, たつや
発行日: 2017年 2月 2日
出版者: The Physical Society of Japan 一般社団法人 日本物理学会
引用: Risa Yoshida, Tomoyuki Kimoto, and Tatsuya Uezu : Journal of the Physical Society of Japan; 2017, Vol. 86 Issue 2, pp.034001-1-034001-1-26
抄録: 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.
記述: 本文データの公開は出版日(2017年2月2日)の12ヶ月後の2018年2月2日となる。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。
???metadata.dc.relation.doi???: http://dx.doi.org/10.7566/JPSJ.86.034001
URI: http://hdl.handle.net/10935/4565
ISSN: 00319015
出現コレクション:雑誌

このアイテムの引用には次の識別子を使用してください: http://hdl.handle.net/10935/4565

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