Condensation of eigen microstate in statistical ensemble and phase transition

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英文篇名：Condensation of eigen microstate in statistical ensemble and phase transition 作者：GaoKe ; Hu ; Teng ; Liu ; MaoXin ; Liu ; Wei ; Chen ; XiaoSong ; Chen 英文作者：GaoKe Hu;Teng Liu;MaoXin Liu;Wei Chen;XiaoSong Chen;Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences;School of Physical Sciences, University of Chinese Academy of Sciences;State Key Laboratory of Information Photonics and Optical Communications & School of Science, Beijing University of Posts and Telecommunications;State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences;School of Systems Science, Beijing Normal University; 英文关键词：statistical ensemble;;eigen microstate;;condensation;;phase transition;;finite-size scaling 中文刊名：JGXG 英文刊名：中国科学:物理学 力学 天文学(英文版) 机构：Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences;School of Physical Sciences, University of Chinese Academy of Sciences;State Key Laboratory of Information Photonics and Optical Communications & School of Science, Beijing University of Posts and Telecommunications;State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences;School of Systems Science, Beijing Normal University; 出版日期：2019-04-26 09:39 出版单位：Science China(Physics,Mechanics & Astronomy) 年：2019 期：v.62 基金：supported by the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZD-SSW-SYS019);; supported by the HPC Cluster of ITP-CAS 语种：英文; 页：JGXG201909004 页数：8 CN：09 ISSN：11-5849/N 分类号：45-52

摘要

In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M →∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M →∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.
        In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M → ∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M → ∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.

引文

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