Phase Transitions, Broken Symmetry and the Renormalization Group

Authored by: Stephen J. Blundell

The Routledge Handbook of Emergence

Print publication date:  March  2019
Online publication date:  March  2019

Print ISBN: 9781138925083
eBook ISBN: 9781315675213
Adobe ISBN:

10.4324/9781315675213-20

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Abstract

A piston is pushed into a cylinder and compresses a gas. The pressure goes up as the volume goes down, in accordance with Boyle’s law. In such a simple thermodynamic description, it is not necessary to worry about what is going on at the atomic scale. Nor do we need to concern ourselves with the fact that this simple lab experiment is being carried out on the surface of planet Earth, a 12,800-km-diameter rotating sphere filled with iron and coated with a silicate crust. Nor is our Boyle’s law analysis using the fact that such a rotating sphere glides along its orbit through largely empty space. Nor indeed do we need to keep in mind that the galaxy in which the solar system resides is an unusually high-density region of the universe. Just as our thermodynamics experiment can be performed in a lab without fussing over such cosmological niceties, a cosmologist in the office next door who is studying the Friedmann model of the expansion of the universe will take the average mass density of the universe (equivalent to around a few protons per cubic metre) as a simple parameter. She will blissfully ignore the “clumpiness” of matter at smaller scales, and of course will neglect the presence of the experiment with the piston and the cylinder of gas sitting on planet Earth.

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