Multifractal and Network Analysis of Phase Transition

Abstract

Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate how far a system is from a critical threshold. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the fluctuation and geometrical structures of magnetization time series of two-dimensional Ising model around critical point. The Hurst exponent has been confirmed to be a good indicator of phase transition. Increase of the multifractality of the time series have been observed from generalized Hurst exponents and singularity spectrum. Both Long-term correlation and broad probability density function are identified to be the sources of multifractality of time series near critical regime. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties of magnetization time series from complex network perspective. Evolution of the topology quantities such as clustering coefficient, average degree, average shortest path length, density, assortativity and heterogeneity serve as early warnings of phase transition. Those methods and results can provide new insights about analysis of phase transition problems and can be used as early warnings for various complex systems.

23 pages, 11 figures

References in corpus (14)

• Statistical physics of social dynamics
• From time series to complex networks: the visibility graph
• Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series
• Multifractal detrended cross-correlation analysis for two nonstationary signals
• Detrending moving average algorithm for multifractals
• Detrended fluctuation analysis for fractals and multifractals in higher dimensions
• Multifractal analysis of Chinese stock volatilities based on partition function approach
• Fractal Markets Hypothesis and the Global Financial Crisis: Scaling, Investment Horizons and Liquidity
• Algorithm to estimate the Hurst exponent of high-dimensional fractals
• Early warning signs in social-ecological networks
• Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant
• Behavior of early warnings near the critical temperature in the two-dimensional Ising model
• Statistical early-warning indicators based on Auto-Regressive Moving-Average processes
• Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models

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