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Elements of Phase Transitions and Critical Phenomena$
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Hidetoshi Nishimori and Gerardo Ortiz

Print publication date: 2010

Print ISBN-13: 9780199577224

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780199577224.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 17 April 2021

Random systems

Random systems

(p.178) 8 Random systems
Elements of Phase Transitions and Critical Phenomena

Hidetoshi Nishimori

Gerardo Ortiz

Oxford University Press

Real materials always contain randomness or disorder that cannot be expressed by idealized simple model systems. The present chapter studies the effects of randomness on phase transitions and critical phenomena. Although randomness may seem to obscure singular behaviour such as divergence of physical quantities at the critical temperature, it is established that well-defined phase transitions exist as long as randomness is not too strong, but the critical behaviour may get modified with respect to the pure sample. After the introduction of basic concepts and methods such as self-averaging and replica method, it is elucidated what type of phase transitions exist in the random-field Ising model and the SK model of spin glasses. Also explained are the percolation transitions using the fractal structure and the Potts model.

Keywords:   randomness, disorder, self-averaging, spin glass, SK model, replica method, percolation, fractal structure, Potts model

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