Publications associated with Quantum Matter in High Magnetic Fields

Phase transitions, broken symmetry and the renormalization group

in The Routledge Handbook of Emergence, (2019) 237-247

SJ Blundell

© 2019 selection and editorial matter, Sophie Gibb, Robin Findlay Hendry, and Tom Lancaster. All rights reserved. The renormalization group should probably be called the renormalization semigroup, but sometimes, contradictory terminology sticks. The renormalization group procedure provides important insights because it shows quantitatively how fine-scale structure is progressively ignored and the physics of critical phenomena depend on these larger-scale, what students might call "structural", features of the theory. The renormalization group breaks big problems down into small ones. Broken symmetry can be seen as a well-studied paradigm of emergent behaviour in the physical world. By breaking symmetry, these phases forfeit the status of being a "stationary state" of the sort beloved of elementary quantum mechanics treatments. Phase transitions are sharp and there is a clear delineation between the ordered and disordered states. The set of symmetry-breaking phase transitions includes as members those between the ferromagnetic and paramagnetic states and those between the superconducting and normal metal states of certain materials.

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