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Phase Transitions and Renormalization Group

Jean Zinn-Justin

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book provides 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 ... More


INDEX THEOREM ON THE LATTICE AND CHIRAL ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Recent progress in the treatment of Dirac fields in lattice gauge theory has allowed the chiral symmetry and associated anomaly on the lattice to be discussed in a manner similar to that in continuum ... More


Directed Random Growth Models on the Plane

Timo Seppäläinen

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0001
Subject:
Mathematics, Probability / Statistics, Analysis

This chapter discusses random growth models describing the evolution of an interface in the plane. For specific models, three basic questions are discussed. First, under appropriate scaling, what is ... More


Classical statistical physics: One dimension

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter, within the framework of classical statistical mechanics, discusses a family of models defined on one-dimensional lattices. It studies the simplest local examples: models that involve ... More


Universality and the continuum limit

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the related questions of universality and macroscopic continuum limit in random systems with a large number of degrees of freedom. It first explains the notion of universality ... More


CLASSICAL AND QUANTUM STATISTICAL PHYSICS

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter provides a simple physical interpretation to the formal continuum limit that has led, from an integral over position variables corresponding to discrete times, to a path integral. It ... More


Continuum limit and path integrals

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter shows that, as in the case of the random walk, one can associate to the continuum limit a path integral, which generalizes the path integral of the Brownian motion. It first studies the ... More


Back to the Schrödinger equation on a lattice

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter goes back to the discrete lattice in order to transform the basis to momentum eigenstates. In addition, the chapter takes the continuum limit of space and we recover known relations and ... More


The random walk: Universality and continuum limit

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The first chapter discusses the asymptotic properties at large time and space of the familiar example of the random walk. The universality of a large scale behaviour and, correspondingly, the ... More


From Random Walks to Random Matrices

Jean Zinn-Justin

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models ... More


Continuous systems

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes how the arguments in the previous part, which worked on discrete systems, can be generalized to the continuum limit. After reviewing Hamilton’s formulation of classical ... More


A digest of matrix models

Razvan Gurau

in Random Tensors

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198787938
eISBN:
9780191829918
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198787938.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

There are many excellent reviews on random matrices both in mathematics and in physics literature. This chapter presents only a very quick overview of some selected topics in random matrix theory: ... More


The perturbative expansion of tensor models

Razvan Gurau

in Random Tensors

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198787938
eISBN:
9780191829918
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198787938.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents the perturbative expansion of invariant tensor measures in terms of Feynman graphs. It is shown that, assuming that the perturbation and the Gaussian part scale at the same rate ... More


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