Author : Uwe C. Täuber
Publisher : Cambridge University Press
Page : 529 pages
File Size : 21,75 MB
Release : 2014-03-06
Category : Science
ISBN : 0521842239
A comprehensive and unified introduction to describing and understanding complex interacting systems.
Author : Jan H. Stockemer
Publisher :
Page : 0 pages
File Size : 39,80 MB
Release : 2016
Category :
ISBN :
Author : Peter Kopietz
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 24,70 MB
Release : 2010-05-03
Category : Language Arts & Disciplines
ISBN : 364205093X
This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.
Author : W. D. McComb
Publisher : Oxford University Press
Page : 349 pages
File Size : 39,50 MB
Release : 2004
Category : Business & Economics
ISBN : 0198506945
This text fills a gap between undergraduate and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation, proceeds to the epsilon-expansion and ends with the first-order corrections to critical exponents beyond mean-field theory.
Author : J. J. Binney
Publisher : Oxford University Press
Page : 477 pages
File Size : 44,97 MB
Release : 1992-06-11
Category : Science
ISBN : 0191660566
The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.
Author : Nigel Goldenfeld
Publisher : CRC Press
Page : 417 pages
File Size : 41,10 MB
Release : 2018-03-08
Category : Science
ISBN : 0429962045
Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Author : Mucio Continentino
Publisher : Cambridge University Press
Page : 249 pages
File Size : 29,15 MB
Release : 2017-04-17
Category : Science
ISBN : 1107150256
Focusing on experimental results, this updated edition approaches the problem of quantum phase transitions from a new and unifying perspective.
Author : Roberto Fernandez
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 35,87 MB
Release : 2013-03-14
Category : Science
ISBN : 3662028662
Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.
Author : John Cardy
Publisher : Cambridge University Press
Page : 264 pages
File Size : 25,25 MB
Release : 1996-04-26
Category : Science
ISBN : 9780521499590
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
Author : Giorgio Benedek
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 17,12 MB
Release : 2012-12-06
Category : Science
ISBN : 3642821359
The investigation of the properties of nonlinear systems is one of the fast deve loping areas of physics. In condensed matter physics this 'terra incognita' is approached from various starting points such as phase transitions and renormali zation group theory, nonlinear models, statistical mechanics and others. The study of the mutual interrelations of these disciplines is important in developing uni fying methods and models towards a better understanding of nonlinear systems. The present book collects the lectures and seminars delivered at the workshop on "Statics and Dynamics of Nonlinear Systems" held at the Centre for SCientific Culture "Ettore Majorana·" in Erice;· Italy, July 1 to 11, 1983, in the framework of the International School of Materials Science and Technology. Experts and young researchers came together to discuss nonlinear phenomena in condensed matter physics. The book is divided into five parts, each part containing a few general artic les introducing the subject, followed by related specialized papers. The first part deals with basic properties of nonlinear systems including an introduction to the general theoretical methods. Contrfbutions to the nonlinear aspects of phase transitions are collected in the second part. In the third part properties of incommensurate systems are discussed. Here, competing interactions lead to charge-density waves, soliton lattices and other complex structures. Another point of special interest, illustrated in the fourth part, is the 'chaotic' be havior of various systems such as Josephson junctions and discrete lattices.
