Critical Phenomena in Natural Sciences

Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications.
The second edition is a significant expansion over the first one which meanwhile has become a standard reference in complex system research and teaching: Probability concepts are presented more in-depth and the sections on Lévy laws and the mechanisms for power laws have been greatly enlarged. Much material has been added to the chapter on renormalisation group ideas. Further improvements can be found in the applications to earthquake or rupture models. TOC:Useful Notions of Probability Theory.- Sums of Random Variables, Random Walks and the Central Limit Theorem.- Large Deviations.- Power Law Distributions.- Fractals and Multifractals.- Rank-Ordering Statistics and Heavy Tails.- Statistical Mechanics: Probabilistic Point of View and the Concept of "Temperature".- Long-Range Correlations.- Phase Transitions: Critical Phenomena and First-Order Transitions.- Transitions, Bifurcations and Precursors.- The Renormalization Group.- The Percolation Model.- Rupture Models.- Mechanisms for Power Laws.- Self-Organized Criticality.- Introduction to the Physics of Random Systems.- Randomness and Long-Range Laplacian Interactions.