Phase Transitions and Renormalization Group by Jean Zinnjustin

Phase Transitions and Renormalization Group by Jean Zinnjustin

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.

A subject of lasting importance, presented by one of the best qualified authors internationally* John Chalker, University of Oxford *
The topic is good, with renewed interest in the renormalization group by the new generation of string theorists and particle theorists. * Randall Kamien, University of Pennsylvania *
This book is highly recmmendable * Journal of Statistical Physics *

Professor Jean Zinn-Justin Head of Department, Dapnia, CEA/Saclay, France

SKU	Unavailable
ISBN 13	9780199227198
ISBN 10	0199227195
Title	Phase Transitions and Renormalization Group
Author	Jean Zinnjustin
Series	Oxford Graduate Texts
Condition	Unavailable
Binding Type	Hardback
Publisher	Oxford University Press
Year published	2007-07-05
Number of pages	466
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.