SKU: 23948880777

Complexity & Criticality (V1)

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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.
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SKU: 23948880777

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Ruth
Chelsea, US
★★★★★ 4
The best for crate training
Color: White
Crate trained our new puppy the 1st night I put this in his crate! I highly recommend! Great quality! The back is just a little hard to open to turn the heartbeat on and off.
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Reviewed in the United States on August 31, 2025
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Melappel
Lake Worth, US
★★★★★ 5
Perfect for my pup
Color: White, Color: White
At first I thought this was going to have a cheap quality and an uncomfortable fur like material but I was soo wrong. This stuffed animal is light weight but the first night my 9 week old bernedoodle slept with it, he fell asleep so quick and it was the first time he didn’t cry in the time we have had him. He loves to cuddle with this stuffy during nap time and when the heartbeat is on, he doesn’t chew it which is crazy because he loves chewing on stuffed animals. If you are even considering getting this, I 100% recommend pulling the trigger. Love love love it and it is a new necessity in our house
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Reviewed in the United States on February 19, 2024
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Michele
Draper, US
★★★★★ 5
Nice quality , works well
Color: White
Washable, does exactly what it says . Place the plastic heart inside and it works. If you want to turn it off , locate the button while it’s still inside and press and it turns it off
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Reviewed in the United States on June 7, 2025
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VRD
Waukegan, US
★★★★★ 5
Calm and Happy
Color: White
My new puppy lives her emotional support toy. After the first 2 nights, she was yelling this toy showed up and immediately calmed our nights. Now she attacks it as if she's still with her siblings.
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Monica
Omaha, US
★★★★★ 5
durable
Color: cow
my dogs 1 german shepherd and 1 beagladoor absolutely love this toy. they are constantly fighting over it. Good news it is very durable, held up about a month now and still holding strong
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Reviewed in the United States on April 7, 2026

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