Series Expansion Methods for Strongly Interacting Lattice Models

By: Jaan Oitmaa, Chris Hamer, Weihong Zheng

Write A Review

Hardcover | 6 April 2006

At a Glance

Hardcover
338 Pages

Dimensions(cm)
24.41 x 16.99 x 2.06

Hardcover

RRP $259.95

$226.75

13%OFF

or 4 interest-free payments of $56.69 with

or

Ships in 5 to 7 business days

Perturbation series expansion methods are sophisticated numerical tools used to provide quantitative calculations in many areas of theoretical physics. This book gives a comprehensive guide to the use of series expansion methods for investigating phase transitions and critical phenomena, and lattice models of quantum magnetism, strongly correlated electron systems and elementary particles. Early chapters cover the classical treatment of critical phenomena through high temperature expansions, and introduce graph theoretical and combinatorial algorithms. The book then discusses high-order linked-cluster perturbation expansions for quantum lattice models, finite temperature expansions, and lattice gauge models. Also included are numerous detailed examples and case studies, and an accompanying resources website, www.cambridge.org/9780521842426, contains programs for implementing these powerful numerical techniques. A valuable resource for graduate students and postdoctoral researchers working in condensed matter and particle physics, this book will also be useful as a reference for specialized graduate courses on series expansion methods.

Industry Reviews

"The present book is unique as it combines a pedagogical approach to series expansion techniques with modern applications in quantum systems. The authors succeed in making this technical subject attractive for newcomers... the book can be recommended to any researcher who wishes to learn series expansion techniques." Michel Pleimling, Mathematical Reviews

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Physics

A Short History of Nearly Everything 2.0

Paperback

RRP $36.99

$29.75

20%
OFF

The Return of the God Hypothesis

Three Scientific Discoveries Revealing the Mind Behind the Universe

Paperback

RRP $36.99

$29.75

20%
OFF

The Breath of the Gods

The History and Future of the Wind

Paperback

RRP $37.99

$28.99

24%
OFF

The Body Electric : Electromagnetism and the Foundation of Life - Robert O. Becker

$22.99

15%
OFF

The Invisible Rainbow

A History of Electricity and Life

Paperback

RRP $60.01

$38.75

35%
OFF

The Holographic Universe - Michael Talbot

$29.75

17%
OFF

The Modern Energies : Jenny Stanford Series on Renewable Energy - Wolfgang Palz

$126.75

$482.75

12%
OFF

Alchemy of Nine Dimensions

Activating the Full Spectrum of Consciousness

Paperback

RRP $32.99

$26.99

18%
OFF

Our Universe - An Astronomer's Guide : An Astronomer's Guide - Jo Dunkley

$288.75

11%
OFF

High Order Methods and Applications in Computational Mechanics : Fluid Mechanics and Its Applications - Rakesh Ranjan

$26.75

16%
OFF

Physics for Beginners

For Beginners

Hardcover

RRP $19.99

$18.75

Zinn and the Art of Mountain Bike Maintenance, 7th Edition

The World's Best-Selling Guide to Mountain Bike Repair

Paperback

RRP $49.99

$42.99

14%
OFF

Preface	p. viii
Introduction	p. 1
Lattice models in theoretical physics	p. 1
Examples and applications	p. 1
The important questions	p. 10
Series expansion methods	p. 14
Analysis of series	p. 19
High- and low-temperature expansions for the Ising model	p. 26
Introduction	p. 26
Graph generation and computation of lattice constants	p. 30
A case study: high-temperature susceptibility for the Ising model on the simple cubic lattice	p. 36
Low-temperature expansion	p. 39
Reducing the number of graphs	p. 42
More on Ising models	p. 47
Models with continuous symmetry and the free graph expansion	p. 53
Introduction	p. 53
The free graph expansion	p. 55
The plane rotator (N = 2) model	p. 66
Analysis of the N = 2 susceptibility	p. 69
Discussion	p. 72
Quantum spin models at T = 0	p. 74
Introduction	p. 74
Linked cluster expansions	p. 74
An example: the transverse field Ising model in one dimension	p. 78
Magnetization and susceptibility	p. 82
One-particle excitations	p. 84
The transverse field Ising model in two and three dimensions	p. 92
Quantum antiferromagnets at T = 0	p. 99
Introduction: simple antiferromagnets	p. 99
Dimerized systems and quantum phase transitions	p. 106
The J[subscript 1]-J[subscript 2] square lattice antiferromagnet	p. 112
Other systems	p. 118
Open questions	p. 122
Correlators, dynamical structure factors and multi-particle excitations	p. 124
Introduction	p. 124
Two-spin correlators for the Heisenberg antiferromagnet	p. 125
Dynamical and static structure factors	p. 126
Two-particle and multi-particle excitations	p. 134
Two-particle structure factors	p. 145
Summary and further work	p. 147
Quantum spin models at finite temperature	p. 150
Introduction	p. 150
Derivation of high-temperature series	p. 151
The cubic (SC and BCC) lattices	p. 165
Generalizations	p. 168
Perturbation expansions at finite T	p. 169
Further applications	p. 175
Fitting to experimental data	p. 176
Electronic models	p. 179
Introduction	p. 179
The Hubbard model	p. 180
The t-J model	p. 197
Further topics and possibilities	p. 209
Review of lattice gauge theory	p. 211
Quantum chromodynamics	p. 211
The path integral approach to field theory	p. 214
Euclidean lattice gauge theory	p. 217
Confinement and phase structure on the lattice	p. 219
Renormalization theory and the continuum limit	p. 221
Monte Carlo simulations	p. 222
Including fermions on the lattice	p. 225
The Hamiltonian lattice formulation	p. 227
Conclusions	p. 228
Series expansions for lattice gauge models	p. 230
Strong coupling expansions for Euclidean lattice Yang-Mills theory	p. 230
Strong coupling expansions in Hamiltonian Yang-Mills theory	p. 244
Models with dynamical fermions	p. 251
The t-expansion	p. 259
Conclusions	p. 263
Additional topics	p. 265
Disordered systems	p. 265
Other series expansion methods	p. 274
Some graph theory ideas	p. 283
The 'pegs in holes' algorithm	p. 286
Free graph expansion technicalities	p. 288
Matrix perturbation theory	p. 291
Matrix block diagonalization	p. 294
The moment-cumulant expansion	p. 297
Integral equation approach to the two-particle Schrodinger equation	p. 299
Correspondences between field theory and statistical mechanics	p. 304
Computer programs	p. 307
Bibliography	p. 311
Index	p. 324
Table of Contents provided by Ingram. All Rights Reserved.

Series Expansion Methods for Strongly Interacting Lattice Models

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Physics

A Short History of Nearly Everything 2.0

The Return of the God Hypothesis

Three Scientific Discoveries Revealing the Mind Behind the Universe

The Breath of the Gods

The History and Future of the Wind

The Body Electric

Electromagnetism and the Foundation of Life

A Brief History Of Time

From Big Bang to Black Holes

The Invisible Rainbow

A History of Electricity and Life

The Holographic Universe

Gravitational-Wave Astronomy Ogt Paperback

Exploring the Dark Side of the Universe

Rotating Disc Cavity Flow and Heat Transfer

Wiley-ASME Press Series

Black Holes

The key to understanding the universe

The Modern Energies

Jenny Stanford Series on Renewable Energy

Dynamic Characteristics of Layered Structures

Mathematical Modelling and Numerical Simulations

Low-Temperature Combustion Strategies

Fundamentals and Applications

Computational Mineral Physics

A Practical Guide for Earth Scientists

Electron

A Biography

Microalgal Biofuels

Biotechnology and Biorefineries

Alchemy of Nine Dimensions

Activating the Full Spectrum of Consciousness

Our Universe - An Astronomer's Guide

An Astronomer's Guide

Introduction and Applications of Machine Learning in Geotechnics

High Order Methods and Applications in Computational Mechanics

Fluid Mechanics and Its Applications

A New Science of Heaven

How the new science of plasma physics is shedding light on spiritual experience

Astrophysics for People in a Hurry

Physics for Beginners

For Beginners

Zinn and the Art of Mountain Bike Maintenance, 7th Edition

The World's Best-Selling Guide to Mountain Bike Repair

This product is categorised by