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Complexity and Criticality

Kim Christwnsen

Imperial College Press

Release Date
2022-11-08

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 5/5

In Stock

2.0 $

Category
Earth Science

File Type
Book

Language
English

File Format
PDF

Year
2005

ISBN-10
186094504X

ISBN-13
9781860945045

Pages
206 pages

File Size
21.969 MB

Release Date
2022-11-08

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Book Summary

The “Complexity and Criticality” book provides a challenging and stimulating introduction to the contemporary topics of complexity and criticality, and explores their common basis of scale invariance, a central unifying theme of the book. Criticality refers to the behaviour of extended systems at a phase transition where scale invariance prevails. The interactions of numerous microscopic components give rise to macroscopic phenomena that elude comprehension when studying individual parts in isolation. The book introduces phase transitions phenomenology through percolation, a simple model with a purely geometrical phase transition. This approach helps readers intuitively grasp concepts such as scale invariance and renormalization. Following that, we introduce the Ising model, which captures a thermodynamic phase transition from disorder to order as temperature decreases without an external field. By drawing analogies between percolation and the Ising model, the book fosters readers’ understanding of phase transitions, facilitating a comprehensive appreciation of the underlying theoretical framework.

Exactly tuned external parameters are necessary for phase transitions in equilibrium systems to occur. In addition to fractals and phase transitions, Nature exhibits complex behavior in slowly driven non-equilibrium systems, such as earthquakes in seismic systems, avalanches in granular media, and rainfall in the atmosphere. Non-equilibrium systems, exempt from the need for precise external parameter tuning, are explored through simple models. These models reveal that the iterative application of straightforward rules can spontaneously generate intricate emergent behavior not explicitly defined in the rules themselves.

The “Complexity and Criticality”book identifies the shared foundation of complexity and criticality and applies it to various non-equilibrium systems. It encourages readers to ponder whether self-organization in these systems could serve as a unifying concept across diverse fields, including statistical mechanics, geophysics, and atmospheric physics.