9780199665167-0199665168-Phase Transitions and Renormalization Group (Oxford Graduate Texts)

Phase Transitions and Renormalization Group (Oxford Graduate Texts)

ISBN-13: 9780199665167
ISBN-10: 0199665168
Edition: Illustrated
Author: Zinn-Justin, Jean
Publication date: 2013
Publisher: Oxford University Press
Format: Paperback 464 pages
FREE shipping on ALL orders

Book details

ISBN-13: 9780199665167
ISBN-10: 0199665168
Edition: Illustrated
Author: Zinn-Justin, Jean
Publication date: 2013
Publisher: Oxford University Press
Format: Paperback 464 pages

Summary

Acknowledged authors Zinn-Justin, Jean wrote Phase Transitions and Renormalization Group (Oxford Graduate Texts) comprising 464 pages back in 2013. Textbook and eTextbook are published under ISBN 0199665168 and 9780199665167. Since then Phase Transitions and Renormalization Group (Oxford Graduate Texts) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

This work tries to provide an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, we will emphasize the role of gaussian distributions and their relations with the mean field approximation and Landau's theory of critical phenomena. We will show that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. We will assign this difficulty to the coupling of very different physical length scales, even though the systems we will consider have only local, that is, short range interactions. To analyze the unusual situation, a new concept is required: the renormalization group, whose fixed points allow understanding the universality of physical properties at large distance, beyond mean-field theory. In the continuum limit, critical phenomena can be described by quantum field theories. In this framework, the renormalization group is directly related to the renormalization process, that is, the necessity to cancel the infinities that arise in straightforward formulations of the theory. We thus discuss the renormalization group in the context of various relevant field theories. This leads to proofs of universality and to efficient tools for calculating universal quantities in a perturbative framework. Finally, we construct a general functional renormalization group, which can be used when perturbative methods are inadequate.

Rate this book Rate this book

We would LOVE it if you could help us and other readers by reviewing the book