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

Morales IO, Landa E, Angeles CC, Toledo JC, Rivera AL, Temis JM, Frank A - PLoS ONE (2015)

Bottom Line: Several early-warning signals have been reported in time series representing systems near catastrophic shifts.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.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México, D.F., México; Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, México, D.F., México; Laboratorio Nacional de Ciencias de la Complejidad, D.F., México.

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.

No MeSH data available.


Temporal kurtosis as a function of temperature.Ensemble behavior of the kurtosis as a function of temperature. Three regimes are shown, T < Tc, T ≈ Tc and T > Tc.
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pone.0130751.g006: Temporal kurtosis as a function of temperature.Ensemble behavior of the kurtosis as a function of temperature. Three regimes are shown, T < Tc, T ≈ Tc and T > Tc.

Mentions: Fig 6 shows the kurtosis of the distribution. It is clear that this moment is a good early warning for this system regardless of the direction in which the system approaches criticality. Kurtosis behaves quite symmetrically and increases smoothly when coming from either direction. The only difference is whether the distribution is more strongly peaked or not than the reference normal distribution (which has a kurtosis of 3). When approaching criticality from lower temperatures we have a strongly peaked or leptokurtic distribution, while when doing so from higher temperatures we have a flattened or platykurtic distribution.


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

Morales IO, Landa E, Angeles CC, Toledo JC, Rivera AL, Temis JM, Frank A - PLoS ONE (2015)

Temporal kurtosis as a function of temperature.Ensemble behavior of the kurtosis as a function of temperature. Three regimes are shown, T < Tc, T ≈ Tc and T > Tc.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4477971&req=5

pone.0130751.g006: Temporal kurtosis as a function of temperature.Ensemble behavior of the kurtosis as a function of temperature. Three regimes are shown, T < Tc, T ≈ Tc and T > Tc.
Mentions: Fig 6 shows the kurtosis of the distribution. It is clear that this moment is a good early warning for this system regardless of the direction in which the system approaches criticality. Kurtosis behaves quite symmetrically and increases smoothly when coming from either direction. The only difference is whether the distribution is more strongly peaked or not than the reference normal distribution (which has a kurtosis of 3). When approaching criticality from lower temperatures we have a strongly peaked or leptokurtic distribution, while when doing so from higher temperatures we have a flattened or platykurtic distribution.

Bottom Line: Several early-warning signals have been reported in time series representing systems near catastrophic shifts.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.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México, D.F., México; Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, México, D.F., México; Laboratorio Nacional de Ciencias de la Complejidad, D.F., México.

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.

No MeSH data available.