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The method of the renormalization group (RG) provides theorists with powerful and efficient tools to explore interacting theories, often in regimes where perturbation theory fails. Finally, to conclude this chapter, we visit a number of concrete implementations of the RG program introduced and exemplified on a number of canonical applications. We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Email your librarian or administrator to recommend adding this book to your organisation's collection. The idea of scale transformations and scale invariance is old in physics: Scaling arguments were commonplace for the Pythagorean school, Euclid, and up to Galileo. Close this message to accept cookies or find out how to manage your cookie settings. However, from a critical perspective, one may say that such perturbative approaches present only a limited understanding. In Chapter 5, ø4-theory was introduced as an archetypal model of interacting continuum theories. The method of the renormalization group (RG) provides theorists with powerful and efficient tools to explore interacting theories, often in regimes where perturbation theory fails. But what controls the validity of the low-order expansion? the ø4-continuum description was obtained as a gradient expansion of, in that case, a d-dimensional Ising model. They became popular again at the end of the 19th century, perhaps the first example being the idea of enhanced viscosity of Osborne Reynolds, as a way to explain turbulence. With this background, we then proceed to discuss the idea and practice of RG methods in more rigorous and general terms, introducing the notion of scaling, dimensional analysis, and the connection to the general theory of phase transitions and critical phenomena. PHYSICS 268BR: Renormalization Group Methods in Condensed Matter Physics. Firstly, the validity of the ø4-action as a useful model theory was left unjustified, i.e. We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Motivating our discussion with two introductory examples drawn from a classical and a quantum theory, we first become acquainted with the RG as a concept whereby nonlinear theories can be analyzed beyond the level of plain perturbation theory. Motivated by the existence of nonlinearities inherent in the model, a full perturbative scheme was developed, namely Wick contractions and their diagrammatic implementation. PHYSICS 268BR: Renormalization Group Methods in Condensed Matter Physics. Field Theories of Condensed Matter Physics - February 2013. Check if you have access via personal or institutional login. Indeed, the same question could be applied to any one of the many continuum approximations we have performed throughout the first chapters of the text.

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