*JEAN ZINN-JUSTIN*

- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780198509233
- eISBN:
- 9780191708732
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509233.003.0028
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Many systems to which the RG predictions based on the φ4 field theory apply are non-magnetic. This chapter considers three systems or classes of systems which are of special interest because they ...
More

Many systems to which the RG predictions based on the φ4 field theory apply are non-magnetic. This chapter considers three systems or classes of systems which are of special interest because they allow precise comparisons between RG results, experiments and simulations: long polymer chains (self-avoiding random walks), liquid-vapour, and superfluid Helium. It shows that their critical properties are indeed related to the N-component φ4 field theory: N = 0 describes the statistical properties of polymer chains asymptotically when the length becomes large, N = 1 and N = 2 the universal properties of the liquid-vapour and Helium super fluid transitions, respectively.Less

Many systems to which the RG predictions based on the φ^{4} field theory apply are non-magnetic. This chapter considers three systems or classes of systems which are of special interest because they allow precise comparisons between RG results, experiments and simulations: long polymer chains (self-avoiding random walks), liquid-vapour, and superfluid Helium. It shows that their critical properties are indeed related to the *N*-component φ^{4} field theory: *N* = 0 describes the statistical properties of polymer chains asymptotically when the length becomes large, *N* = 1 and *N* = 2 the universal properties of the liquid-vapour and Helium super fluid transitions, respectively.

*Jean Zinn-Justin*

- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780198509233
- eISBN:
- 9780191708732
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509233.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The book is an introduction to quantum field theory and renormalization group. It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of ...
More

The book is an introduction to quantum field theory and renormalization group. It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This book emphasizes the common aspects of particle physics and the theory of critical phenomena in a unified framework. Three new chapters have been included in this edition: an introduction to non-relativistic quantum statistical physics; a chapter on critical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chapter on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted to critical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory.Less

The book is an introduction to quantum field theory and renormalization group. It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This book emphasizes the common aspects of particle physics and the theory of critical phenomena in a unified framework. Three new chapters have been included in this edition: an introduction to non-relativistic quantum statistical physics; a chapter on critical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chapter on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted to critical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory.