Book review:
Quantum Saling in Many-Body Systems, by Muio A. Continentino
(WorldSienti, Singapore, 2001;188pp.; ISBN981-02-4389-8)
L.N.Oliveira
InstitutodeFsiade S~aoCarlos,Universidade deS~aoPaulo
CaixaPostal369,13560-970S~aoCarlos,SP, Brazil.
Thenotion of saleinvarianehas alonghistory. It permeatesthe work of Jonathan Swift, and wasapplied
to uiddynamis alreadyin the19thentury. Thirty-veyearsago,whenmoderntheoriesof ritialphenomena
wereforged,itwasraisedto anewstatus: ritialexponentsomparedso favorablywith experimentsthatin the
theorists' eyesallpreviousappliationsoftheanientoneptbeamepale. Viewedfromthelaboratory,however,
omparisonsthatwererestritedtotheviinityofritialpointsseemednarrow,andsalingbegantoberegarded
as auriosityinthejunkyardoftheoretialphysis. MuioContinentinohangedthat outlook.
Inaseriesofpapersinthelateeightiesandearlynineties,heandhisollaboratorsshowedthatsalinganalyses
helpedidentifyquantumritialpointsinthephasediagramsofavarietyofstronglyorrelatedsystemsthatdeed
thepoweroftraditionalmany-bodytheories. Theirsystematiworkshedlightonfaetsthathadbeenignoredand
thusprovidedqualitativeunderstandingforanumberofdiÆultproblems. Hehasnowsummarizedhisexperiene
in aslenderhardover.Youmaywellwantto havethisvolumeonyourdesk.
Bewarethe buyer, this is noprimer for freshmangraduate students. Even advaned dotoral andidates are
likelytotakeinlessthanhalfofwhatthebookisworth,beausemuhiswritten betweenthelines. Thisisnotto
saythat thetextis tooterse,orthealgebraimpenetrable.
On the ontrary, the reasoningis easy to follow, and the author has beenmetiulous in presenting suÆient
mathematial detail that a student with adequate trainingon Quantum and StatistialMehanis aneasily
re-produeeah derivation. Astheexperienedwriterknows,however,derivationsand mathematialargumentstell
only halfthe story. Theauthor tellstheother halfby meansofshort sentenes drawingattentiontothe
implia-tionsofthemathematialresults. Thebestpassagesarebriefparagraphs,loadedwith physialinsight,whihthe
readermustexpandin his/hermind. Carryingoutsuhexpansionsis,ofourse, instrutive,but someexperiene
isrequired.
Anotherstimulatingaspetofthework istheauthor'semphasisonthesimpliityandgeneralityofthesaling
approah. Fromtheoutset, hemakesit learthat thederivation ofasaling relationalls for a
renormalization-grouptransformation. Asthetext evolves,heappliesthesameapproahtodierentexamples,to lassialand to
quantummodels,tonearlytrivialHamiltoniansandtoomplexones. Thispatternisathreadthatbindstogether
thetwelvehaptersofthebook. Anotherthread istheauthor'sattentionto Goldstonemodes. An opportunityis
nevermissedtoidentifyanddisussthemodeassoiatedwithanappliation,andthatispartoftherihnessofthe
book.
There isyet another unifying feature. Inalmost everyhapter,the authorhas agure, anequation, oraset
of equationsthat epitomizesthedisussion. Figure1.2and Eq.(2.11), forinstane, summarizeChapters1and2,
respetively. Onegets used tothis pattern, and ndingthe epitome andseeing howitenapsulates almostevery
aspetof ahapter beomesoneof thejoysofreadingthebook.
Thetexthasothervirtues. Muhofitsstrengthstemsfromitsstruture. Ave-hapterfoundationisfollowed
byappliations,toheavyfermions,tometal-insulatortransitions,tothenon-linearsigmamodel,andto
superon-dutors. The rst part,whih inludes a formalintrodution, disusses lassialand quantum phasetransitions.
The treatmentis standard,similar to thatfound in by-nowlassialbooks. Hindsightandthe author'sextensive
rst-handexperienewithsalingnonethelessmakethosedisussionsremarkablyrih. Theonlyo-beatnoteisthe
hapterdediated toreal-spae renormalization-grouptransformations. Aspointedoutbytheauthor,suh
trans-formationshaveasimpliitythatappealstothoseinterestedinsalingtehniques;inpratie,however,deimation
tehniqueshavelongbeensupersededby SteveWhite'sDensity-MatrixRenormalization-Group approah. Not to
ndWhite's workin thebibliographyisdisappointing.
Thesubsequenthapters,onheavyfermions,areexellent. Here theauthorombinestheoryandexperimental
data to omposewhat reads likeadetetivestory. In onehapter he presents thelues: experimental datathat
formerhapteristurned, expetnorespitepriortoreadingthelastpageofthelatterone.
Alsooutstanding are thethree hapters on the metal-insulator transition. Conepts are adequatelylaid out,
with emphasisonthe distintionbetweendensity-drivenand orrelation-induedtransitions. The twotransitions
arethendisussedindetail. Thehapter\Density-DrivenMetal-InsulatorTransitions",withitsopeningdisussion
ofanon-interatingbandisasentiingas itisilluminating. Figure10.1epitomizestheentirethree-hapterunit.
Thefollowinghapter,\TheNon-LinearSigmaModel",mightapthebook. Combiningeasy-to-grasponepts
withmathematial expressionsthat remindthereaderofthose seenin previouspages,and learlyrepresentedby
Fig.11.1, it would servewellthe purpose of summarizing thetext. The author,however, hose to add atwelfth
hapter,17pagesdediatedto quantum superondutortransitions. Here hehasanumberofinterestingpointsto
make,buttheresultseemspoorlyintegratedwiththepreedingtext. Superondutivityisavastsubjet,andthe
author'sonernwithlengthtakesatollthatdetratsfromtheharmonyofthework.
All in all, the book is nonetheless very attrative. To those who would prefer a more vigorous style, the
author oersanotherrhythm,of longhapters thatalternate with short ones,andabstrat setionsbak-to-bak
withonreteexamples. ThosewithlessexperienewilllikeContinentino'sunpretentiousproseandhis sympathy
towardsthereader.
Leavethebookontheshelfifyoulaktheneessarypreparation,orifyoudonotlikeondensedmatterphysis.
Read it, otherwise. Chanes are that you will be a better physiist by the time you turn the last page. A few
hapters before that, you may feel the urge to feth penil and paper, to pursue ideasthat pop in yourmind. I
experiene that feeling, and it reminded me of a sene in At IV of ShakespearesKing Henry V, the monarh's
speehto hissoldiersbeforethebattleofAginourt: ofthisspeeh itissaidthat,whenthemonologueisnished,
