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

PLoS One. 2015 Jun 23;10(6):e0130751. doi: 10.1371/journal.pone.0130751. eCollection 2015.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Chemistry, Physical
  • Computer Simulation*
  • Magnetic Phenomena*
  • Models, Chemical*
  • Monte Carlo Method
  • Phase Transition*
  • Stochastic Processes
  • Temperature*
  • Time

Grants and funding

This work was supported by Universidad Nacional Autónoma de México-Dirección General de Asuntos del Personal Académico-Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica IA100914 project. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.