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Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model

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  • Irving O Morales
  • Emmanuel Landa
  • Carlos Calderon Angeles
  • Juan C Toledo
  • Ana Leonor Rivera
  • Joel Mendoza Temis
  • Alejandro Frank

Abstract

Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point.

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  • Irving O Morales & Emmanuel Landa & Carlos Calderon Angeles & Juan C Toledo & Ana Leonor Rivera & Joel Mendoza Temis & Alejandro Frank, 2015. "Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-20, June.
    • Handle: RePEc:plo:pone00:0130751
    DOI: 10.1371/journal.pone.0130751
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    References listed on IDEAS

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    1. Fatimah Abdul Razak & Henrik Jeldtoft Jensen, 2014. "Quantifying ‘Causality’ in Complex Systems: Understanding Transfer Entropy," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-14, June.
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    1. Orozco-Fuentes, S. & Griffiths, G. & Holmes, M.J. & Ettelaie, R. & Smith, J. & Baggaley, A.W. & Parker, N.G., 2019. "Early warning signals in plant disease outbreaks," Ecological Modelling, Elsevier, vol. 393(C), pages 12-19.

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