Statistical Mechanics Algorithms and Computations W Krauth.pdf
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1、OXFORD MASTER SERIES IN STATISTICAL,COMPUTATIONAL,AND THEORETICAL PHYSICSOXFORD MASTER SERIES IN PHYSICSThe Oxford Master Series is designed for final year undergraduate andbeginning graduate students in physics and related disciplines.It hasbeen driven by a perceived gap in the literature today.Whi
2、le basicundergraduate physics texts often show little or no connection with thehuge explosion of research over the last two decades,more advancedand specialized texts tend to be rather daunting for students.In thisseries,all topics and their consequences are treated at a simple level,while pointers
3、to recent developments are provided at various stages.The emphasis in on clear physical principles like symmetry,quantummechanics,and electromagnetism which underlie the whole of physics.At the same time,the subjects are related to real measurements and tothe experimental techniques and devices curr
4、ently used by physicists inacademe and industry.Books in this series are written as course books,and include ample tutorial material,examples,illustrations,revisionpoints,and problem sets.They can likewise be used as preparation forstudents starting a doctorate in physics and related fields,or for r
5、ecentgraduates starting research in one of these fields in industry.CONDENSED MATTER PHYSICS1.M.T.Dove:Structure and dynamics:an atomic view of materials2.J.Singleton:Band theory and electronic properties of solids3.A.M.Fox:Optical properties of solids4.S.J.Blundell:Magnetism in condensed matter5.J.
6、F.Annett:Superconductivity,superfluids,and condensates6.R.A.L.Jones:Soft condensed matterATOMIC,OPTICAL,AND LASER PHYSICS7.C.J.Foot:Atomic physics8.G.A.Brooker:Modern classical optics9.S.M.Hooker,C.E.Webb:Laser physics15.A.M.Fox:Quantum optics:an introductionPARTICLE PHYSICS,ASTROPHYSICS,AND COSMOLO
7、GY10.D.H.Perkins:Particle astrophysics11.Ta-Pei Cheng:Relativity,gravitation and cosmologySTATISTICAL,COMPUTATIONAL,AND THEORETICALPHYSICS12.M.Maggiore:A modern introduction to quantum field theory13.W.Krauth:Statistical mechanics:algorithms and computations14.J.P.Sethna:Statistical mechanics:entrop
8、y,order parameters,andcomplexityStatistical MechanicsAlgorithms and ComputationsWerner KrauthLaboratoire de Physique Statistique,Ecole NormaleSup erieure,Paris13Great Clarendon Street,Oxford OX2 6DPOxford University Press is a department of the University of Oxford.It furthers the Universitys object
9、ive of excellence in research,scholarship,and education by publishing worldwide inOxford NewYorkAuckland CapeTown DaresSalaam HongKong KarachiKualaLumpur Madrid Melbourne MexicoCity NairobiNewDelhi Shanghai Taipei TorontoWith offices inArgentina Austria Brazil Chile CzechRepublic France GreeceGuatem
10、ala Hungary Italy Japan Poland Portugal SingaporeSouthKorea Switzerland Thailand Turkey Ukraine VietnamOxford is a registered trade mark of Oxford University Pressin the UK and in certain other countriesPublished in the United Statesby Oxford University Press Inc.,New Yorkc?Oxford University Press 2
11、006The moral rights of the author have been assertedDatabase right Oxford University Press(maker)First published 2006All rights reserved.No part of this publication may be reproduced,stored in a retrieval system,or transmitted,in any form or by any means,without the prior permission in writing of Ox
12、ford University Press,or as expressly permitted by law,or under terms agreed with the appropriatereprographics rights organization.Enquiries concerning reproductionoutside the scope of the above should be sent to the Rights Department,Oxford University Press,at the address aboveYou must not circulat
13、e this book in any other binding or coverand you must impose the same condition on any acquirerBritish Library Cataloguing in Publication DataData availableLibrary of Congress Cataloging in Publication DataData availablePrinted in Great Britainon acid-free paper byCPI Antony Rowe,Chippenham,Wilts.IS
14、BN 0198515359(Hbk)9780198515357ISBN 0198515367(Pbk)978019851536410 9 8 7 6 5 4 3 2 1F ur Silvia,Alban und FelixThis page intentionally left blank PrefaceThis book is meant for students and researchers ready to plunge intostatistical physics,or into computing,or both.It has grown out of myresearch ex
15、perience,and out of courses that I have had the good fortuneto give,over the years,to beginning graduate students at the Ecole Nor-male Sup erieure and the Universities of Paris VI and VII,and also tosummer school students in Drakensberg,South Africa,undergraduatesin Salem,Germany,theorists and expe
16、rimentalists in Lausanne,Switzer-land,young physicists in Shanghai,China,among others.Hundreds ofstudents from many different walks of life,with quite different back-grounds,listened to lectures and tried to understand,made comments,corrected me,and in short helped shape what has now been writtenup,
17、for their benefit,and for the benefit of new readers that I hope toattract to this exciting,interdisciplinary field.Many of the students satdown afterwards,by themselves or in groups,to implement short pro-grams,or to solve other problems.With programming assignments,lackof experience with computers
18、 was rarely a problem:there were alwaysmore knowledgeable students around who would help others with thefirst steps in computer programming.Mastering technical coding prob-lems should also only be a secondary problem for readers of this book:allprograms here have been stripped to the bare minimum.No
19、ne exceeda few dozen lines of code.We shall focus on the concepts of classical and quantum statisticalphysics and of computing:the meaning of sampling,random variables,ergodicity,equidistribution,pressure,temperature,quantum statisticalmechanics,the path integral,enumerations,cluster algorithms,and
20、theconnections between algorithmic complexity and analytic solutions,toname but a few.These concepts built the backbone of my courses,andnow form the tissue of the book.I hope that the simple language andthe concrete settings chosen throughout the chapters take away none ofthe beauty,and only add to
21、 the clarity,of the difficult and profoundsubject of statistical physics.I also hope that readers will feel challenged to implement many ofthe programs.Writing and debugging computer code,even for the naiveprograms,remains a difficult task,especially in the beginning,but it iscertainly a successful
22、strategy for learning,and for approaching the deepunderstanding that we must reach before we can translate the lessons ofthe past into our own research ideas.This book is accompanied by a compact disc containing more than onehundred pseudocode programs and close to 300 figures,line drawings,viiiPref
23、aceand tables contained in the book.Readers are free to use this mate-rial for lectures and presentations,but must ask for permission if theywant to include it in their own publications.For all questions,pleasecontact me at www.lps.ens.fr/?krauth.(This website will also keep alist of misprints.)Read
24、ers of the book may want to get in contact witheach other,and some may feel challenged to translate the pseudocodeprograms into one of the popular computer languages;I will be happyto assist initiatives in this direction,and to announce them on the abovewebsite.Contents1Monte Carlo methods11.1Popula
25、r games in Monaco31.1.1Direct sampling31.1.2Markov-chain sampling41.1.3Historical origins91.1.4Detailed balance151.1.5The Metropolis algorithm211.1.6A priori probabilities,triangle algorithm221.1.7Perfect sampling with Markov chains241.2Basic sampling271.2.1Real random numbers271.2.2Random integers,
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