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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

(p.83) 4 Implementation of the renormalization group
Elements of Phase Transitions and Critical Phenomena

Hidetoshi Nishimori

Gerardo Ortiz

Oxford University Press

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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