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9 - Monte Carlo renormalization group methods

Published online by Cambridge University Press:  24 November 2021

David Landau  and
Kurt Binder
David Landau
Affiliation:
University of Georgia
Kurt Binder
Affiliation:
Johannes Gutenberg Universität Mainz, Germany
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Summary

The concepts of scaling and universality presented in Chapter 2 can be given a concrete foundation through the use of renormalization group (RG) theory. The fundamental physical ideas underlying RG theory were introduced by Kadanoff (1971) in terms of a simple coarse-graining approach, and a mathematical basis for this viewpoint was completed by Wilson (1971). Kadanoff divided the system up into cells of characteristic size ba, where a is the nearest neighbor spacing, and ba < ξ , where ξ is the correlation length of the system (see Fig. 9.1). The singular part of the free energy of the system can then be expressed in terms of cell variables instead of the original site variables, i.e.

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Chapter
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A Guide to Monte Carlo Simulations in Statistical Physics , pp. 416 - 429
Publisher: Cambridge University Press
Print publication year: 2021

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