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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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Implementation of the renormalization group

Implementation of the renormalization group

Chapter:
(p.83) 4 Implementation of the renormalization group
Source:
Elements of Phase Transitions and Critical Phenomena
Author(s):

Hidetoshi Nishimori

Gerardo Ortiz

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199577224.003.0004

Actual computations of fixed points and eigenvalues usually involve approximations, often crude ones, except for a very limited number of simple cases such as the one-dimensional Ising model of the previous chapter. In real- and momentum-space renormalization group theory, there are no general prescriptions to systematically improve the degree of the approximation with a modest amount of effort. There are established methods to systematically improve precision, but they usually need a large amount of numerical calculations. The scope of the present chapter is modest as we limit ourselves to basic examples, including the epsilon expansion about the Gaussian fixed-point of the Landau-Ginzburg-Wilson model. Finally, the last section illustrates the extension of the renormalization group framework to study quantum phase transitions.

Keywords:   Ising models, LGW model, epsilon expansion, renormalization group theory, quantum phase transition

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