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Andrew M. Steane

Print publication date: 2016

Print ISBN-13: 9780198788560

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198788560.001.0001

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Continuous phase transitions

Continuous phase transitions

(p.355) 25 Continuous phase transitions

Andrew M. Steane

Oxford University Press

The general phenomenon of continuous phase transitions is discussed, and treated by the Landau mean field approach. First some illustrative examples are discussed, and the concepts of order parameter and critical exponents are introduced. The critical exponents for the liquid–vapour critical point of a van der Waals gas are obtained. Then the Landau mean field theory is described for a generic system, showing how the competition between entropy and internal energy affects the free energy. Critical exponents are obtained, and the static scaling hypothesis briefly mentioned. The results are then applied to ferromagnetism and to binary mixtures. Eutectic behaviour is introduced.

Keywords:   Order parameter, Landau mean field, critical exponent, static scaling hypothesis, ferromagnet, binary mixture, eutectic

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