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Description
Complexity & Criticality (V1)This 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 many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part
This 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 many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part alone. The phenomenology of phase transitions is introduced by considering percolation, a simple model with a purely geometrical phase transition, thus enabling the reader to become intuitively familiar with concepts such as scale invariance and renormalisation. The Ising model is then introduced, which captures a thermodynamic phase transition from a disordered to an ordered system as the temperature is lowered in zero external field. By emphasising analogies between percolation and the Ising model, the reader's intuition of phase transitions is developed so that the underlying theoretical formalism may be appreciated fully. These equilibrium systems undergo a phase transition only if an external agent finely tunes certain external parameters to particular values.Besides fractals and phase transitions, there are many examples in Nature of the emergence of such complex behaviour in slowly driven non-equilibrium systems: earthquakes in seismic systems, avalanches in granular media and rainfall in the atmosphere. A class of non-equilibrium systems, not constrained by having to tune external parameters to obtain critical behaviour, is addressed in the framework of simple models, revealing that the repeated application of simple rules may spontaneously give rise to emergent complex behaviour not encoded in the rules themselves. The common basis of complexity and criticality is identified and applied to a range of non-equilibrium systems. Finally, the reader is invited to speculate whether self-organisation in non-equilibrium systems might be a unifying concept for disparate fields such as statistical mechanics, geophysics and atmospheric physics.Visit for animations for the models in the book (available for Windows and Linux), solutions to exercises, as well as a list with corrections.Shipping Notes
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Product Reviews
★★★★★ 5
Very versatile table for many uses.
Style: Rectangular, Size: 28 inch
These legs work great for replacing a free standing rv dinette by reusing the table top . We didn’t need a table that converted to a bed. Nice fit and finish and great quality.
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Reviewed in the United States on April 14, 2026
★★★★★ 5
very good
Style: Zig Zag, Size: 28 inch
These are very stable and worked perfectly with our butcher blocks! The size and length are true to what it says! you can adjust height.
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Reviewed in the United States on January 7, 2026
★★★★★ 5
Perfect
Size: 16 Inch
Exactly what I ordered, took just a few minutes to assemble and mount the legs. Love that the bottoms can be manipulated to give a balanced stance.
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Reviewed in the United States on February 23, 2026
★★★★★ 5
Perfect
Size: 16 Inch
Love the sturdieness and the almost stram punk look to these. Great quality and easy to install
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Reviewed in the United States on July 16, 2025
★★★★★ 4
Good Look and Adjustable Heights
Size: 16 Inch
Legs are sturdy enough, but to hold a small marble top, it required additional glue to secure the "wobble." Adjustable height was excellent and material quality good. Easy enough to install and works well for a table that I don't plan to move frequently.
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Reviewed in the United States on May 9, 2025
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