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2 - Dynamical Derivation (and a More Conventional One) of the Mermin–Wagner–Hohenberg Theorem; or, Why We Can’t All Point the Same Way
John Toner, University of Oregon
Book:

The Physics of Flocking

Published online:

16 May 2024

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23 May 2024, pp 9-29
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Summary

I present a purely dynamical derivation of the Mermin–Wagner–Hohenberg theorem, and compare it with the standard equilibrium derivation. This also provides an opportunity to introduce diffusion equations and gradient expansions, both of which play a large role in what follows.

1 - Introduction and Motivation: Are Birds Smarter Than Nerds?
John Toner, University of Oregon
Book:

The Physics of Flocking

Published online:

16 May 2024

Print publication:

23 May 2024, pp 1-8
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Summary

I introduce the problem of “dry active matter” more precisely, describing the symmetries (both underlying, and broken) of the state I wish to consider, and also discuss how shocking it is that such systems can exhibit long-ranged order – that is, all move together – even in d = 2.

Birth, Death, and Flight in Active Matter
John Toner
Published online:

16 May 2024

Print publication:

23 May 2024
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In creatures ranging from birds to fish to wildebeest, we observe the collective and coherent motion of large numbers of organisms, known as 'flocking.' John Toner, one of the founders of the field of active matter, uses the hydrodynamic theory of flocking to explain why a crowd of people can all walk, but not point, in the same direction. Assuming a basic undergraduate-level understanding of statistical mechanics, the text introduces readers to dry active matter and describes the current status of this rapidly developing field. Through the application of powerful techniques from theoretical condensed matter physics, such as hydrodynamic theories, the gradient expansion, and the renormalization group, readers are given the knowledge and tools to explore and understand this exciting field of research. This book will be valuable to graduate students and researchers in physics, mathematics, and biology with an interest in the hydrodynamic theory of flocking.