Chapter

Implementation of the renormalization group

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print December 2010 | ISBN: 9780199577224
Published online January 2011 | e-ISBN: 9780191722943 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199577224.003.0004

Series: Oxford Graduate Texts

Implementation of the renormalization group

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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

Chapter.  10908 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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