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Multifractality and Network Analysis of Phase Transition

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifracta...

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Autores principales: Zhao, Longfeng, Li, Wei, Yang, Chunbin, Han, Jihui, Su, Zhu, Zou, Yijiang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5249085/
https://www.ncbi.nlm.nih.gov/pubmed/28107414
http://dx.doi.org/10.1371/journal.pone.0170467
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author Zhao, Longfeng
Li, Wei
Yang, Chunbin
Han, Jihui
Su, Zhu
Zou, Yijiang
author_facet Zhao, Longfeng
Li, Wei
Yang, Chunbin
Han, Jihui
Su, Zhu
Zou, Yijiang
author_sort Zhao, Longfeng
collection PubMed
description Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems.
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spelling pubmed-52490852017-02-06 Multifractality and Network Analysis of Phase Transition Zhao, Longfeng Li, Wei Yang, Chunbin Han, Jihui Su, Zhu Zou, Yijiang PLoS One Research Article Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. Public Library of Science 2017-01-20 /pmc/articles/PMC5249085/ /pubmed/28107414 http://dx.doi.org/10.1371/journal.pone.0170467 Text en © 2017 Zhao et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Zhao, Longfeng
Li, Wei
Yang, Chunbin
Han, Jihui
Su, Zhu
Zou, Yijiang
Multifractality and Network Analysis of Phase Transition
title Multifractality and Network Analysis of Phase Transition
title_full Multifractality and Network Analysis of Phase Transition
title_fullStr Multifractality and Network Analysis of Phase Transition
title_full_unstemmed Multifractality and Network Analysis of Phase Transition
title_short Multifractality and Network Analysis of Phase Transition
title_sort multifractality and network analysis of phase transition
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5249085/
https://www.ncbi.nlm.nih.gov/pubmed/28107414
http://dx.doi.org/10.1371/journal.pone.0170467
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