Cambridge University Press eBooks

Monte Carlo renormalization group methods

David Paul Landau, Kurt Binder

Published Jul 29, 2021• 0 citations

Abstract

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.

DOI: 10.1017/9781108780346.010

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