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

Morales, Irving O.; Landa, Emmanuel; Angeles, Carlos Calderon; Toledo, Juan C.; Rivera, Ana Leonor; Temis, Joel Mendoza; Frank, A.

doi:10.1371/journal.pone.0130751

Cited by 17 publications

(45 citation statements)

References 47 publications

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“…Simulation results have confirmed the existence of phase transition around the theoretical critical temperature T c ≃ 2.27. This transition can also be verified from three statistical quantities in Fig 2: (b) variance σ 2 , (c) skewness S and (d) kurtosis G which have been fully discussed in Ref [46]. Those moments have been used as early-warnings of phase transition therein.…”

Section: Resultsmentioning

confidence: 59%

“…As a final remark of the paper, we shall emphasize the importance of our previous results from the view of early-warnings [1, 46, 56]. Recently, plenty of early-warnings have been proposed and summarized [1, 46, 48, 57–64].…”

Section: Resultsmentioning

confidence: 83%

“…It is large only in the low temperature region and reaches its maxima at critical point and then becomes very small at high temperature region. This is due to the meta-stable states at low temperature [46]. The stochastic permutation is not strong enough to make the system escape from the meta-stable states.…”

Section: Resultsmentioning

confidence: 99%

“…This indicates that the magnetization time series posses long-range correlations. Those characteristics of the generalized Hurst exponent should be very good early-warnings [1, 46]. …”

Section: Resultsmentioning

confidence: 99%

“…Recently, plenty of early-warnings have been proposed and summarized [1, 46, 48, 57–64]. Those early-warnings can be categorized into two major classes: metric-based indicators which probe the delicate changes in the statistical properties of the time series, and model-based indicators which detect the changes in the time series dynamics fitted by reasonable models.…”

Section: Resultsmentioning

confidence: 99%

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Multifractality and Network Analysis of Phase Transition

Bai¹,

Li²,

Yang³

et al. 2017

PLoS ONE

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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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Section: Resultsmentioning

confidence: 59%

Section: Resultsmentioning

confidence: 83%

Section: Resultsmentioning

confidence: 99%

“…This indicates that the magnetization time series posses long-range correlations. Those characteristics of the generalized Hurst exponent should be very good early-warnings [1, 46]. …”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 3 more Smart Citations

Multifractality and Network Analysis of Phase Transition

Bai¹,

Li²,

Yang³

et al. 2017

PLoS ONE

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Early warning signals in plant disease outbreaks

Orozco-Fuentes¹,

Griffiths²,

Holmes³

et al. 2019

Ecological Modelling

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Infectious disease outbreaks in plants threaten ecosystems, agricultural crops and food trade. Currently, several fungal diseases are affecting forests worldwide, posing a major risk to tree species, habitats and consequently ecosystem decay. Prediction and control of disease spread are difficult, mainly due to the complexity of the interaction between individual components involved. In this work, we introduce a lattice-based epidemic model coupled with a stochastic process that mimics, in a very simplified way, the interaction between the hosts and pathogen. We studied the disease spread by measuring the propagation velocity of the pathogen on the susceptible hosts. Our quantitative results indicate the occurrence of a critical transition between two stable phases: local confinement and an extended epiphytotic outbreak that depends on the density of the susceptible individuals. Quantitative predictions of epiphytotics are performed using the framework early-warning indicators for impending regime shifts, widely applied on dynamical systems. These signals forecast successfully the outcome of the critical shift between the two stable phases before the system enters the epiphytotic regime. Our study demonstrates that early-warning indicators could be useful for the prediction of forest disease epidemics through mathematical and computational models suited to more specific pathogen-host-environmental interactions. Our results may also be useful to identify a suitable planting density to slow down disease spread and in the future, design highly resilient forests.

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