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

Irving O Morales,Carlos Calderon Angeles,Alejandro Frank,Joel Mendoza Temis,Juan C Toledo,Ana Leonor Rivera,Emmanuel Landa,Enrique Hernandez-Lemus

doi:10.1371/journal.pone.0130751

Irving O Morales, Carlos Calderon Angeles + Show 6 more

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https://doi.org/10.1371/journal.pone.0130751

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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.

Highlights

Complex systems are those in which the agents or elements that compose the system interact non-linearly and in such a convoluted way that it is impossible to describe the behavior of the system in terms of the simpler behavior of its components
When the system is near the critical point it exhibits the critical slowing down phenomenon and our numerical experiments demonstrate the deep connection of this behavior with several early-warning signals in the evolution of the magnetization time series
We have shown that the change in these properties is asymmetrical, i.e., it is not the same when the critical point is approached from different directions

Summary

Introduction

Complex systems are those in which the agents or elements that compose the system interact non-linearly and in such a convoluted way that it is impossible to describe the behavior of the system in terms of the simpler behavior of its components. There is no general agreement of what complex systems are. Complex systems share certain general properties which in some fashion describe them: emergence, self-organization, homeostasis, entangled properties on multiple scales, ability to efficiently transmit and process information, etc. In this work we focus on a property that is apparently common to many complex systems: the existence of critical thresholds [5]. A large number of complex systems display behaviors related to criticality and phase transitions [6,7,8]. When a physical system is in a PLOS ONE | DOI:10.1371/journal.pone.0130751 June 23, 2015

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