; TeX output 1995.03.08:15243D̼X3DŧߍNG cmbx12PREPaGARINGzARTICLESWITHzLXUZXQ cmr12ATc EXN cmbx12INSTRUCTIONSTOAUTHORSFORPREPARINGCOMPUSCRIPTSfZ?K`y cmr10ELSEVIERUUSCIENCE N!AmstUe rdramUU-Oxford-NewY*ork-Lausanne-Tokyo*3D̼X3DŧߍPREPaGARINGzARTICLESWITHzLXUZATc EXINSTRUCTIONSTOAUTHORSFORPREPARINGCOMPUSCRIPTSvK`y 3 cmr10ELSEVIERfSCIENCE Amst=e rdamf-Oxford-NewYeork-Lausann!e-Toky!o3D̼X3D!Thi&sfpu2blilcat!ionwastyp&eMs6etusingL|{Ycmr8A4T,[wEB X P T,[wEB Xfi&satradGemarkoft2h!eAme r.ilcanMat2hematilcalfSoMcietyCo!pyr.ightcf"!", 3 cmsy10 @1995fbyEls6evie rScienceFHAllfr.igh!tsreMs6e rvedM3D̼X3D̼+"V 3 cmbx10Content׳s341InXtroMd!uction 5,p0J 3 cmsl105 2Prepar.ingfacompusQcript 562.1Tit2lefan!dauthor 562.2Simpleft=ext 572.3Sect!ionalfunits 582.4Li&sts 582.5Cro%ss-refe renceMs 582.6Mat2h!ematilcalfform2ulas 592.7Th!eoremsfanddGe nitions 5112.8ProMofs 5122.9Lit=e rat!urefreferenceMs 5122.10Tea!bleMsfand gureMs 5132.11Programsfan!dalgor.it2hms 5132.12Largefart!ilcleMs 5142.13Pr.ivdDat=efdGe nit!ions 5142.14Lay!out 5142.15Deviat!ionsff.romstandarddoMcum!enXtstyleMs 5152.16Teec!hnilcalfinformation,andve rs&ionsofLA4T,[wEB X 5153Su2bmitt!ingfacompusQcr.ipt 5173.1Sen!dingfviaelectronilcmail 5173.2Su2bmi&s%sionfondi&sk!ett=e 5184Gett!ingfhelp 518AExampleMs 520C33@3D̼4X3D ͠3D̼X3D̼1.IntroYdtuction"No!wadays,iti&sbecomingmorean!dmorecustomaryforaut2horstot!yp&et2heMir man2usQcr.iptsus&ingsom!ekindofelectronilcdGevicean!dcompMo%s&ingt2hereMsultwit2htsom!et=ext-proMces%s&ingtsystem.Systemst2h!atarequitepMo!pularareT,[wEB Xan!d< LA4T,[wEB X.InordGe rtoas%s&ist< aut2hors< inprepar.ingt2h!eMirpap&e rsforartilcleMspu2bli&sh!eMd#jbyEls6evie rSciencesuchawayt2hatt2heMir lescanb&eus6edtopr.inXt%t2h!eartilclef.rom,wehavedGevelop&eMdLA4T,[wEB Xdocum!enXtstyleMsforourjour&nals.WTh!efollowingi&sadGeMsQcr.iptionoft2heMs6edocum!enXtstyleMs.Feorb&estun!dGe rstanding,$Haut2horsshouldb&ere%asona!blyf&amiliarwit2hth!eLA4T,[wEB Xmanualwr.itt=enfb!yLeMslieLamport[1y].fgInordGe rtoena!blet2hepu2bli&she rtobr.ingt2h!eartilcleinXtot2heuniformlayoutan!dIstyleoft2hejour&nalinwhilchitwillapp&e%ar,aut2horsarekindlyrequeMst=edtofollo!wt2hesuggeMstionsmenXtioneMdb&elow.Thi&shast2headvdDanXtageofkeep-ingqeMditor.ialc!hangeMstoaminim2um,whilc!hwillcons&idGe rablysp&eeMdupt2hepu2blilcat!ionfproMces%s.UpMon/receiptoft2h!ecompusQcr.ipt,iti&sgiventoat=echnilcaleMditor,whopr.inXtst2h!ecompusQcr.iptonpap&e r,re%adsitcarefullyandmakeMschangeMswhenne-ceMs%sarye.LIfs6en!dingproofsi&spartoft2h!enormalproced!urefort2hepartilcularjour&nal,yaproMofiss6enXttot2h!eaut2hor.Ifth!eauthor n!dssomet2hinginth!eproMofBt2h!atshouldb&echangeMd,he/sheshouldindilcat=et2hi&scle%arlyinth!emar-gin,Ksot2h!atth!et=echnilcaleMditorcanapplyt2heMs6ecorrectionsb&eforemakingt2h!efpap&e rre%adyforpublilcat!ion.Feoralljour&nalst2h!atacceptauthor-prepareMdLA4T,[wEB Xart!ilclesw!ehavedoMcumenXtst!yleMs.EAllt2heMs6edocum!enXtstyleMs,whilchareus6eMdfort2heactualproMductionoft2h!ejour&nals,havet2hesamecommands.Feurt2he rmore,t2he rei&sas6eparat=edoMcum!enXt~6style- cmmi10 ^ٓRcmr7+*,EC)[f*romPt(p,xn)Aquor...Th!eprop&e rpMo%sit!ionoft2hekeywordenvironmenXti&sinsideit2hefrontmatteren!vironmenXt,fb&eforeoraft=e rt2h!eabstractenvironmenXt.2.2.SimpletextÍTeextshouldb&et!ypeMdasusual.Hyph!ensaretyp&eMdas-,n2umobe rrangeMsaret!yp&eMdas--. .Theendash--i&salsous6eMd,e.g.,in`TheoremofCanXtor{Sc!hrfodGe r{Ber&nst=eMin'.Emph!as&izeMdxt=extisobt!aineMdxwit2hth!ecommand\em.Inmo%stcas6eMst2hi&swillreMsult }init!alilct=extrepres6enXt!ingemphas&is. }Italilct=extshouldb&ete rminateMdb!yfanitalilccorrection,i.e.{\emheavyquarks\/}unleMs%st2h!et=extinitalilcsi&simmeMdiat=elyfolloweMdbyafullstop(.)orcomma(,).Extraorexcept!ionalhyphenationsareaddGeMdtoT,[wEB X'sli&stofabbreviat=eMdw!ordsMbyme%ansoft2hecommand\hyphenation,whilchshouldb&eplaceMdint2h!efpre%amobleofth!edoMcumenXt.Anexample:\hyphenation{caus-almin-i-mi-za-tionpro-ven}InXtroMd!ucemacro%s(wit2hcare,s6ee2.13)fornot!ationsandabbreviationst2hatoMccur,moret2h!anonce,forexample`e.g.'and`i.e.'.Thi&sfacilit!at=eMschangeMsin"not!ation.IfyouinXtroMducemacro%sforabbreviations,t2heMs6eareoft=enpara-m!et=e rleMs%sFqmacros,soy!oushouldb&eawareofT,[wEB X'sb&ebhaviourwit2hregardtospaceMsfollo!wingaparamet=e rleMs%smacro.Aninstructionwit2houtparamet=e rsshouldfb&edGe n!eMdandus6eMdas,3D̼8X3D̼\newcommand{\ie}{i.e.} ......extraparticles,\ie{}particles... X...Oextrapart!ilcleMs,i.e.Xpart!ilcleMsf...I/ҍAlt=e r&nat!iveMsJto\ie{}are\ie\ an!d{\ie}.The\ aft=e r\ieproMducesJa space,fwh!e re%as\ie particleswillreMsultin`i.e.partilcleMs'[1y,p.16].aPutt!ingfaspaceint2hedGe nitionof\iei&snott2her.ightsolution,s&inceitcanreMsultfinaspaceb&eforeapunct!uationfmark,e.g.\newcommand{\ie}{i.e.}......extraparticles,\ie,particles...X... Iextrapart!ilcleMs,i.e.,Xpart!ilcleMsf...O2.3.SepctionalunitsaSect!ionalunitsareobtaineMdint2heusualwaye,i.e.wit2hth!eLA4T,[wEB Xin-stru!ctionsQ\section,\subsection,\subsubsection,\paragraphan!d\subparagraph.An!ewenvironmenXtack{s6eealsoSection2.7{hasb&eenaddGeMdtoprod!ucean'`Ac!knowleMdgemenXts's6ection,whilchshouldb&eplaceMdatt2heendoft2heart!ilcle,fjustb&eforet2herefe renceMs..2.4.ListsaLi&stsSofit=emsareproMd!ucedSwit2hth!eusualitemizeandenumerateenvir-onm!enXts."TheSitemizeen!vironmentSi&sus6eMdforunn2umobe reMdSlistsan!dt2heenumerateչen!vironmenXtforn2umob&e reMdlists.Ev!enift2helayoutoft2heMs6eli&stsi&snotprecis6elywh!atyouwouldlike,weprefe rli&ststobecoMdGedt2hisw!ayinst=e%adofb!yhand.Thi&senableMst2hedoMcumenXtstylefort2hesp&eci cjournaltofdGet=e rmin!et2heli&stlayout.2.5.Crposs-referencesaUs6ea\labelan!d\refforcro%ss-refe renceMsatoequations, gureMs,tableMs,s6ec-t!ions,su2b%s6ections,etc.,inst=e%adofplainn2umob&e rs.Feorrefe renceMstot2h!elit=er-at!urefli&statt2h!eendoft2heartilcles6eeSection2.9.aEv!e ry\label{eq:euler} 9ՠ3D̼bf9X3D̼\end{equation}$Wit2h,th!einstruction\refonecanrefe rtoan2umob&e reMdpartt2h!athasb&een la!b&elleMd:...,seealsoeq.(\ref{eq:euler})Th!ef\labelinstructionshouldb&etyp&eMdbimm!eMdiat=ely?afte r(oron!elineb&elow),butnot insidet2heargumenXtofan2umob&e r-gen!eratinginstructionsuchas\sectionor\caption,e.g.:\caption{Crosssection} T\label{fig:crosssec}؍roughlyint2h!epMo%s&itionwhe ret2hen2umob&e rapp&e%ars,inenvironmenXtssu!chfasequation,e.g.:\begin{equation}'{e^{i\pi}+1=0>\label{eq:euler}\end{equation}2.6.MathematicpalformulasFeorXpin-lin!eform2ulasus6e\(...\)Xpor$...$.AvoidXpbuilt-upconstruc-t!ions,fforexamplef.ractionsandmatr.ilceMs,inin-lineform2ulas.Feorkunn2umob&e reMddisplay!eMdone-lineform2ulasus6eth!edisplaymathenviron-m!enXt;Tort2heshort2handnotation\[... T\].Feorn2umob&e reMddisplay!eMdone-lin!efform2ulasus6eth!eequationenvironmenXt.bDonotus6e$$...$$,fbutonlyYQt2h!eLA4T,[wEB XenvironmenXts,sot2hatt2hedoMcumenXtstyledGet=e rmineMst2hefor-m2ulaflay!out.Feorexample,th!einputfor:u cmex10#X2 b> 3 cmmi10PB+Saȉfe & tVn02gx񩒫Ro(Vnb) =RT;Z (1)i&s:\begin{equation}\left(P+\frac{a}{V^2}\right)(V-b)=RT,\end{equation}Feordi&splay!eMdm2ulti-lineform2ulasus6eth!eeqnarrayenvironmenXt. ,Feorex-ample,\begin{eqnarray}f(x)&=&\sum_{n=1}^{\infty}a_n\cos(nx)+5b_n\sin(nx)\nonumber\\R&=&\sum_{n=-\infty}^{\infty}c_n\exp(-\mathrm{i}xn)\,.\end{eqnarray}proMd!uces: E;3D̼10X3DRc58f-(x)z=C1e#K cmsy81 ύӅC0X   2cmmi8n=1azn{co%sC(nx)n+bzn{s&in%(nx)"DKz=C1:1 ύAßC0X : n=1|czn{exp6.(ixn)1:Z (2)!AngleQ$brac!kets,whilchareus6eMdin,e.g.,t2heinne rproMductnotation,t2he`bra-k!et'5notation(phys&ilcs),andinBNF5(comput=e rsQcience),areobtaineMdwit2h \langlefan!d\rangle:\langlex,y>\rangle=0\langlep|A|p'\rangle=0\langle\mbox{sign}\rangle\longrightarrow+|-Xhx;1ydi =0XhpjAjp09i =0Xhs&ign>i ! +jI\bSup&e rsQcr.iptsan!dsu2b%scr.iptst2h!atarewordsorabbreviations,asinȮloÎw !ӹ,shouldfb&et!ypeMdasromanlett=e rs;t2hisisdon!easfollows:\(\sigma_{\mathrm{low}}\)XȮloÎw inst=e%adfof\(\sigma_{low}\)XȮlKowTh!emo%stcommonsymobMolst2hatareconvenXtionallytyp&eMs6etinaroman t!yp&eface,forexampleunits,areli&st=eMdbelo!w.Feorsomeoft2heMs6e,seealsoTea!blef1onpage16.ETh!efEule rn2umob&er,forexample,exH. iwh!enus6eMdasimaginaryunit,e.g.aS{+biorei,etc.TheEule requation,whilc!hfwasus6eMdasanexamplee%arlie r,cant2he reforealsob&etyp&eMdas\begin{equation}'{\mathrm{e}^{\mathrm{i}\pi}+1=02\label{eq:euler}\end{equation}Geom!etr.ilcfunctions,e.g.exp,s&in,co%s,tan,etc.LA4T,[wEB XprovidGeMsmacro%s\sin,_\cos,\tanfort2h!eMs6eands&imilarfunctions.TheMs6emacro%salsogiv!eft2heprop&e rspacinginmat2hematilcalfform2ulas.Th!edi e renXtialop&e rators,e.g.dx,andt2heop&e ratorsImandRefort2heimaginaryfan!dre%alpartsofcomplexn2umob&e rs,reMspect!ivelye.M2Group%s,fforexampleSU(2)an!dSU(3).La!b&elsfforatomilcorbitalsandatomilcshells.Example:4s,4p,K,L.J:-=2Th9e?normalshap eofGreekcapitallet3te rsi supr'xight.TheslanteAdshap eof,e.g.,tThelet3te r Ti sobt9aineAdTwitTh9ߤN cmtt9\varDelta,asin1 cmsy9AuAM]>S-L5ADFTuAEX:05" cmmi9. N3D̼] ̹11X3D̼Greekflett=e rswh!enus6eMdasaunit,e.g. forohm.Unitsfingen!e ral.Example:cm,bA,andbforbar&n.Su2b%sQcr.iptsٻan!dsup&e rscr.iptst2h!atareus6eMdasanabbreviation.Ex- ampleMs:wTC (Cur.iet=emp&e rat!ure),Tzc B(crit!ilcalt=emp&e rature),andCz3v(idGenXt!i e rfofspacegroup)Op&e ratorZorfunct!ionnameMs,ort2heMirabbreviatons,e.g.Ke r,Im,Hom,Re,fet!c.g.Oft2h!eadvdDanceMdfe%atureMsofT,[wEB XwemenXtiont2hepMo%ss&ibilitytodGe neextrasymobMols.Extrarelat!ionsymbMolscanb&edGe n!edasint2h!efollowingexample(s6eefalsoSect!ion2.13):k9\newcommand{\leL}{\mathrel{\le_{\mathrm{L}}}}\(a\leLb\)proMd!ucesft2hefollowingreMsult:џa LhbExtraflog-lik!efunctionsorop&e ratorscanbedGe n!eMdasfollows:\newcommand{\re}{\mathop{\mathrm{Re}}} \newcommand{\im}{\mathop{\mathrm{Im}}}\(z+\bar{z}=2\rez, T\quad>z-\bar{z}=2\mathrm{i}\imz\)proMd!ucesft2hefollowingreMsult:џz5+Pnz |= 21Rez{I; fzPnz= 2i1ImzFeorymoreinformat!iononT,[wEB X'sadvdDanceMdmat2h!emat!ilcalyfe%atureMsywerefe rto c!hapt=e rs16{18oft2h!eT,[wEB XbMook[3y].Iti&salsopMo%ssibletous6et2h!eA,[wM S-LA4T,[wEB XvJpac!klage[4y],whic!hcanb&eobtaineMdf.romt2heA,[wM S,f.romvdDariousT,[wEB Xarc!hiveMs,forf.romus(s6eeSect!ion4).+t2.7.Theporemsandde nitionsLA4T,[wEB Xopro!vidGeMs\newtheoremtocre%at=et2heoremenvironmenXts.TheEls6evie rdoMcum!enXtgstylesgconXtainas6etofpre-dGe neMdenvironmenXtsfort2heorems,dGe nit!ions,fproMofs,remarksandt2helike.џTh!efollowingenvironmenXtsaredGe neMd(analogoustot2heexamplegivenint2h!efA,[wM S-LA4T,[wEB Xus6e r'sguidGe[4y,x31.5]): [٠3D̼12X3DVR)Љffe En!vironmenXtfnamef;*He%adingJ} ffdEn!vironmenXtfname He%adingzffethmf;*Th!eoremt } ffdexmp Example lemf;*Lemma} ffdprob Problemcorf;*Corollaryx} ffdrem Remarkpropf;*Pro!pMo%s&ition͟} ffdnote Not=ecritf;*Cr.it=e rionkM} ffdclaim Claimalgf;*Algor.it2hm } ffdsumm Summarydefnf;*De nit!ion } ffdcase Cas6econjf;*Conject!ure .} ffdack Ac!knowleMdgemenXtffeJHnTeoh6addt2h!eorem-typ&eh6environmenXtstoanartilcle,us6et2he\newtheoremcom- man!df{s6eet2heLA4T,[wEB Xus6e rman2ual[1y]..2.8.Prpoofs7hTh!e"Els6evie rdoMcumenXtstyleMsalsoprovidGeapreMde n!ed"pfenvironmenXt,andast!arreMdformpf*,forproofs.Th!epfenvironmenXtproMducest2hehe%ading`ProMof'rwit2hap!propr.iat=erspacingan!dpunct!uation.rA%`Q.E.D.'symobMol,% 3 msam10,canfb&eap!pendGeMdfatt2h!eendofaproMofwit2hth!ecommand\qed.7aTh!ekstarreMdform,pf*,oft2heproMofenvironmenXttakeMsanargumenXtincurlybraceMs,Owhilc!hallowsyoutosu2b%stitut=eadi e renXtnamefort2hestandard`ProMof'.fIfy!ouwanXttosu2b%stitut=e,saye,`ProMof(suciency)',t2henwr.it=e\begin{pf*}{Proof(sufficiency)}2.9.Literpaturereferences7hTh!efli&stoflit=e raturerefe renceMscanb&eprod!ucedfint!wofways,byus&ingt2h!efenvironmenXtthebibliography,or :- 3 cmcsc10BibT,[wEB XExample{[3sho!wsabibliograph!yproMduced{[wit2hth!ethebibliographyen-vironm!enXt.7aIfC t2h!erefe renceMsarecollect=edinon!e,nottoolarge,BibT,[wEB X le(.bib),itw!ould;qb&eappreciat=eMdifyouwouldletushavet2hi&s leaswell.Inafuturerele%as6ePw!ewillincludGeaBibT,[wEB Xbibliographystyleint2heaut2horpacklageasfw!ell.Th!eWinstruction\citeshouldb&eus6eMdtoobtainrefe renceMstot2hi&slist,i.e.cit!ations.TheEls6evie rdoMcumenXtstyleMstakecareoft2heactualformattingoft2h!ecitation,e.g.asromann2umob&e rsbet!weenbrackets,orasasup&e rsQcr.iptn2umob&e r.Feorm2ult!iplecitationsdonotus6e\cite{Knuth}\cite{Lamport},butuse\cite{Knuth,Lamport}inst=e%ad.Cons6ecut!iven2umob&e rsinacit!ationappe%arasRarange,i.e.[1,2,3]i&sautomat!ilcallyconve rt=eMdbyt2hedoMcumenXtstyleto g3D̼] ̹13X3D̼[1{3].\Feoranot=eaddGeMdtoacit!ation\us6e\cite[noteҡ]fkeyg,forexample: \cite[p.217]{Knuth}.b2.10.\keyw{if}extension$(p,x)$>\\u3D̼14X3D̼\>\>\keyw{then}$E:=E\cup\{x\}$\\ \keyw{return}$E$\end{tabbing}wThi&sfproMd!ucesft2hefollowing:ݍforfe%ac!hxdo 5ifext=ens&ion(p;1x)jtyhtenfE9:= E~[nfxgrettur,nfEꪍ2.12.4Questionmark?3D̼18X3D̼%?At>@9Leftbracket[4Backslash?\ %?Rightbracket]9Circumflex^4Underscore_%?Graveaccent `9Leftbrace{4Verticalbar|%?Rightbrace}9Tilde)~䍹Ift2hi&sisincludGeMd,an!ydistort!ioncanbedGet=ecteMdan!dremoveMdf.romt2he su2bmitt=eMdf les.׍3.2.SubmissionondisketteTIfy!ousu2bmityourcompusQcr.iptonadi&skett=e,preparet2he lesucht2hatnolin!eO$i&slonge rt2han72charact=e rs.Terytous6easfewdi&skett=eMsaspo%ss&ible,O$an!dputfala!b&el,wit2h1.nam!efofs6endGe r,and΍2.jour&nalfidGenXt!i cationandartilclen2umob&e ronQe%ac!hoft2hem.Alsoadda lereadmewit2hali&stofallth!e leMsonth!e di&sk!ett=eMsfandadGeMsQcr.iptionoft2heMirconXt=ents.JTh!eLalloweMddi&skett=etyp&eMsare:MS-DOSLV3.5inch,MS-DOSLV5.25inchandMacinXto%sh,fan!dforeve rydi&skett=etyp&ealldGensit!ieMsarepo%ss&ible.%H4.Getttin9g2help"䍹Alt2houghalotofe orth!asb&eenputink!eepingt2h!edoMcum!enXtstylee%asytous6eUYan!dinobtainingaconci&s6edGeMsQcr.iptionoft2hemo%stcommonasp&ectsofst!yle,VUiti&sofcours6epMo%ss&ibleVUt2h!atauthorsencounXt=e rproblemswhileus&ingit.Also aut2horsmigh!thavesuggeMstionsforadditions.Int2ho%s6ecaseMst2h!eyshoulds6en!dEt2heMircommenXtsandsuggeMstionstot2headdreMs%smenXtioneMdont2heins&idGeco!ve rfoft2h!ejour&nal.3<Refe nrenceYs34[1]LeMsliefLamport:LA4T,[wEB X,Adopcumentpreparationsystem,2n!dfeMdition,Addi&son-WeeMsley(Re%ading,Massac!h2us6etts,1994)[2]Milc!hely GoMo%ss6ens,FerankMitt=el!bachandAlexandGe rSamar.in:TheLA4T"R[wE)XComppanion,fAddi&son-WeeMsley(Re%ading,Massac!h2us6etts,1994)[3]DonaldfE.Kn2uth:fTheT"R[wE)XbpookAddi&son-WeeMsleyf(Re%ading,Massac!h2us6etts,1986)[4]A,[wM S-LA4T"R[wE)XGV)ersion1.1|User'sGuide,Am!e r.ilcanMat2hematilcalSoMci-et!ye,!`ProvidGence,R.I.,Decemob&e r1990;distr.ibut=eMdwit2hth!eA,[wM S-LA4T,[wEB Xpac!klage.G3D̼] ̹19X3D̼[5]Ferank]Mitt=el!bachandRaine rSchfopf:The newfontfamilyselepction| userinterfacpetostandardLA4T"R[wE)XTUGboaEtf11(1990)297{305.3D̼20X3D̼A.PExamp.leYs"InYt2hi&sap!pendixYwewillshowafewexampleMsoft2heus6eoft2hedoMcu- m!enXtstyleelsart:twoexampleMsoft2hef.ronXtmatt=e r,andoneexampleof`t2h!ebibliographyenvironmenXt.LA4T,[wEB Xv2z"0,us6e rsshoulds&implysu2b%st!itut=e\documentclassfinplaceof\documentstyle.,3D̼] ̹21X3D̼\documentstyle{elsart} \begin{document}\begin{frontmatter}\title{Integrabilityin(=randommatrixmodels\thanksref{talk}}\thanks[talk]{Expandedversionofatalk TpresentedattheSingaporeMeetingon TParticlePhysics(Singapore,August1990).}\author{L.Alvarez-Gaum\'{e}}\address{TheoryDivision,CERN, TCH-1211Geneva23,Switzerland}\author{C.Gomez\thanksref{SNSF}},\address{D\'{e}partmentdePhysiqueTh\'{e}orique, TUniversit\'{e}deGen\`{e}ve, TCH-1211Geneva4,Switzerland}\author{J.Lacki},\address{SchoolofNaturalSciences, TInstituteforAdvancedStudy, TPrinceton,NJ08540,USA}\thanks[SNSF]{Supportedbythe TSwissNationalScienceFoundation}\begin{abstract}Weprovetheequivalencebetweentherecentmatrixmodelformulationof2Dgravityandlatticeintegrablemodels.ForevenpotentialsthissystemistheVolterrahierarchy.\end{abstract}\end{frontmatter}\section{Introduction}Someaspectsoftherecentlydiscoverednon-perturbativesolutionstonon-criticalstrings\cite{ref1}canbebetterunderstoodandclarifieddirectlyintermsoftheintegrabilitypropertiesoftherandommatrixmodel....NЍExamplef1.Art!ilcleop&eningwit2himplilcitlinks(input).k3D̼22X3DƵ Ingtnegraubilityzinranudomm~atrRixmo=delsg cmmi12?+L.fAlvdDarez-Gaum"De';TheporyDivision,CERN,CH-1211Geneva23,SwitzerlandC.fGom!ez1KLD\eppartmentdePhysiqueTheorique,UniversitedeGeneve,CH-1211 ~Geneva4,SwitzerlandTJ.fLac!ki~@SchopolofNaturalSciences,InstituteforAdvancedStudy,Princeton,NJ ',08540,USAwffh A\rb s-tractW*eftprovetUheequivqalenceb#etweentUherecentmÎatr*ixmoGdTelformUulationof2DgravityoandlatticeintUegrablemoGdTels.F*orevenpGotUentialstUhi#ssystUemistUheV*olrtUe rrahie rarchy*.ffffh"1.2IntroYdtuction"Som!eEBasp&ectsoft2herecenXt2lydi&sQcove reMdnon-p&ert!urbativeEBsolutionstonon-cr.it!ilcalJstrings[1]canb&ebett=e run!dGerstoModJan!dclar.i eMddirect2lyint=e rmsoft2h!efinXt=egrabilityprop&e rtieMsoft2herandommatr.ixmoMdGel.fg...3-=!;cmmi6?ũExpan9d؇eAdpUve rs ionofatalkpreAs. entedattTh9eSingaporeMeet9ingonP9articlePhys ics (SingapAore,TA|rugust1990). -=1?Sup9pAortedTbytTheSwi sNsNationalScienceF:oundationL|Examplef1.Art!ilcleop&eningwit2himplilcitlinks(outřput).>3D̼] ̹23X3D̼\documentstyle{elsart} \begin{document}\begin{frontmatter}\title{Arenormalizationgroupstudyofagauge\\(=theory:SU(3)atfinitetemperature}\author[Madrid]{L.A.Fernandez\thanksref{CAICYT}},\author[Pisa]{M.P.Lombardo},\author[Rome]{R.Petronzio}and\author[Zaragoza]{A.Tarancon\thanksref{CAICYT}}\address[Madrid]{DepartamentodeF\'{\i}sicaTe\'{o}rica, TUniversidadComplutensedeMadrid,E-28040Madrid,Spain}\address[Pisa]{INFN,SezionediPisa,I-56100Pisa,Italy}\address[Rome]{DipartimentodiFisica, TUniversit\`{a}diRomaII``TorVergata''and TINFN,SezionediRomaTorVergata, TViaO.Raimondo,I-00173Rome,Italy}\address[Zaragoza]{DepartamentodeF\'{\i}sicaTe\'{o}rica, TUniversidaddeZaragoza,E-50009Zaragoza,Spain}\thanks[CAICYT]{PartiallysupportedbyCAICYT,Spain.}\begin{abstract}WeapplyafinitesizerenormalizationgroupmethodtothestudyofthedeconfiningtransitioninpuregaugeSU(3).Byconstructingrenormalizedsystemswith$2^3$and2variablessuitablydefinedweobtainaveryaccuratedeterminationofthetransitionpointandofthethermalexponent$\nu$.\end{abstract}\end{frontmatter}ThepuregaugeSU(3)systematfinitetemperatureundergoesaphasetransitionfromtheconfinedtothedeconfinedphaseassociatedtothespontaneousbreakingofthelocalZ(3)symmetry....\vjExamplef2.Art!ilcleop&eningwit2hexplilcitlinks(input).ѭ3D̼24X3D}]lHoO`Azrenorm~alizatuiongroups tudyofagaE`ugeQꍑt0hueory:zSU(3)at nitnetempEeratuure,fչL.A.fFee r&nan!dGeza;1 \|,M.P.Lomobardob8,R.P!etronziocG ,A.Tarancond;1aaDeppartamentodeFssicaT)egCorica,UniversidadComplutensedeMadrid, |KE-28040Madrid,SppainIDbQQINFN,SezionediPisa,I-56100Pisa,ItalyHcDippartimentodiFisica,UniversitgCadiRomaII\T)orVerpgata"andINFN, hSezionediRpomaT)orVerpgata,ViaO.Raimondo,I-00173Rome,Italy 5dDeppartamentodeFssicaT)egCorica,UniversidaddeZaragoza,E-50009{Zarpagoza,Spainwffh A\rb s-tractW*e applya nitUes#izerenormÎalizationgroupmetUhÎoGdtrothestudyoftUhedTecon ninrgtrans#itioninpuregaugeSU(3).ByconstructinrgrenormÎalizeGdsystUemswitUh2^3and2vqar*iableGssuitablydTe neGdweobtainave ryaccuratUedTete rminÎationoftUhetrans#itionUUpGointandoftUhetUhe rmÎalexpGonent.ffffh'3Th!e 8puregaugeSU(3)syst=emat nitetemp&e rat!ureundGe rgo&eMsaphas6etrans-it!ionTf.romt2hecon neMdtot2hedGecon neMdphas6eas%soMciat=edTtot2hespMonXtaneousbre%akingfoft2h!eloMcalZ(3)symmetrye.fg...3-=1?P9artiallyTsuppAortedb9yCAICYT,Spain.ȍExamplef2.Art!ilcleop&eningwit2hexplilcitlinks(outřput).F3D̼] ̹25X3D̼\begin{thebibliography}{9} \bibitem{Robi66}A.Robinson,{\emNon-standardAnalysis\/}(North-Holland,Amsterdam,1966).\bibitem{Sand89a}E.Sandewall,Combininglogicanddifferentialequationsfordescribingreal-worldsystems,in:R.J.Brachmann,H.LevesqueandR.Reiter,eds.,{\emProceedingsFirstInternationalConferenceonPrinciplesofKnowledgeRepresentationandReasoning\/}(MorganKaufmann,LosAltos,CA,1989)412--320.\bibitem{Sand89b}E.Sandewall,Filterpreferentialtreatmentforthelogicofactioninalmostcontinuousworlds,in:R.J.Brachmann,H.LevesqueandR.Reiter,eds.,{\emProceedingsIJCAI-89\/}(Detroit,MI,1989)894--899.\bibitem{Shoh88a}Y.Shoham,Chronologicalignorance:experimentsinnonmonotonictemporalreasoning,{\emArtif.Intell.\/}{\bfseries36}(1988)279--331.\bibitem{Shoh88b}Y.ShohamandD.McDermott,Problemsinformaltemporalreasoning,{\emArtif.Intell.\/}{\bfseries36}(1988)49--61.\bibitem{Bent83}J.vanBenthem,{\emThelogicoftime\/}(Reidel,Dordrecht,1983).\end{thebibliography}3Examplef3.Lit=e rat!urereferenceMs(input).>3D̼26X3D̼Refe nrenceYs34[1]A.xRobinson,Non-standarpd-A\nalysis^(Nort2h-Hollan!d,Amst=e rdam,1966).[2]E.KSan!dGewall,Comobininglogilcanddi e renXtialequationsfordGeMsQcr.ibing re%al-w!orld׿syst=ems,in:R.J.Brachmann,H.LeveMsqueandR.ReMit=e r,eds.,PrpoceedingsT{FirstInternationalConferpenceT{onPrinciplesofKnowFlepdgeRpepresentation8andRpeasoning(MorganKaufmann,Lo%sAltos,CA,1989)412{320.[3]E.jSan!dGewall,Filt=e rpreferenXt!ialtre%atmenXtfort2helogilcofactioninalmo%stconXt!in2uous(Wworlds,in:R.J.Brachmann,H.LeveMsqueandR.ReMit=e r,eds.,PrpoceedingsIJCAI-89"c(Detroit,fMI,1989)894{899.[4]Y.Shoh!am,Chronologilcalignorance:exp&e r.imenXtsinnonmonotonilct=em-pMoralfre%asoning,A\rtif.IntelFl.36(1988)279{331.[5]Y.Shoh!amandD.McDe rmott,Problemsinformalt=empMoralre%asoning,A\rtif.IntelFl.f36(1988)49{61.[6]J.fvdDanBenXt2h!em,Thelopgicoftimey(ReMidGel,fDordrecht,1983).IvrExamplef3.Lit=e rat!urereferenceMs(outřput).圠3D̼X3DȚffIntdEex7ef皚a!bbreviations macro%sffor,7a!b%stract,f6,7abstract,f6ac!knowleMdgemenXts,f8addreMs%s,f6\address,f6o!ptionalfargumenXtof,6algor.it2hm,f13\and,f7anglefbrac!kets,10aut2hor,f6\author,f6o!ptionalfargumenXtof,6#bibliograph!ymadGefwit2hBibT,[wEB X,12madGeRwit2hbibliographyen-(vironm!enXt,f12BibT,[wEB X,f12capt!ion,f13argum!enXtftoMolong,13v!e rtilcalfruleMs,13\caption,f13incomobinat!ionwit2h\label,9cit!ation,f12formatt!ingft2he,12m2ult!iple,f13wit2hfaddGeMdnot=e,13\cite,f12colla!b,f6\collab,f6o!ptionalfargumenXtof,6comput=e rfprogram,13cro%ss-refe rence,f8dash,f7diagram,f13di e renceMsfwit2hst!andardfstyleMs,f6emph!as&izeMdft=ext,7皚ŀenumerate,f8 ŀeqnarrayfen!vironmenXt,9ŀequat!ion,f9ـdi&splay!eMd,f9ـin-lin!e,f9ـm2ult!i-line,f9ŀequationfen!vironmenXt,9ŀextrafinstru!ctions,15xŀfigurefen!vironmenXt,13ـ\labelfin,sepey\captionŀform2ula,f9ـdi&splay!eMd,f9ـin-lin!e,f9ـm2ult!i-line,f9ŀf.ronXtfmatt=e r,6,7ŀh!yphen,f7ŀ\include,f14ŀ\input,f14ŀit!alilcfcorrection,7ŀit!alilcs,f7ŀitemize,f8ŀk!eywordfab%stract,6,7ŀ\label,f8ـforfequat!ionn2umob&e r,9ـforfs6ect!ionalunit,9ـforft!ableor gurecaption,9ŀlay!outـexplilcitfcomman!dsfor,15ŀli&sts,f8ŀlit=e rat!urefreferenceMs,12ŀ\maketitle,f6ŀnot!ationsـmacro%sffor,7ŀn2umob&e rfrangeMs,7ŀparam!et=e rleMs%sfmacro,7f27Ѡ3D̼28X3D̼picture,f13 pre%amoble,f7prooffen!vironmenXt,12\ref,f9romanft!yp&eface,10roMotf le,14\sectionincomobinat!ionwit2h\label,9s6ect!ionalfunits,8spaceexplilcit,f8su2bmitt!ingfacompusQcr.iptonfadi&sk!ett=e,18viafelectronilcmail,17su2b%sQcr.iptsa!bbreviationsfin,10w!ordsfin,10sup&e rsQcr.iptsa!bbreviationsfin,10w!ordsfin,10tablefen!vironmenXt,13\labelfin,sepey\caption\thanks,f6o!ptionalfargumenXtof,6\thanksref,f7t2h!eoremfenvironmenXts,11t!it2le,f6\title,f6units,f10us6e r-dGe n!eMdlog-lik!effunctions,11o!p&e rators,f11relat!ionfsymobMols,11\vec,f15v!ector,f15;3Dh ; 3 cmmi10Aacmr6|{Ycmr8N cmbx12g cmmi12XQ cmr12NG cmbx12K`y 3 cmr10 b> cmmi10K`y cmr10ٓRcmr7u cmex10j