JStatPhys(2011)145:510–517 DOI10.1007/s10955-011-0381-x Cyril Domb: A Personal View and Appreciation MichaelE.Fisher Publishedonline:8November2011 ©SpringerScience+BusinessMedia,LLC2011 It is not given to so many scholars to found and establish an internationally influential “school”inasignificantbranchofScience.ButthatiswhatCyrilDombhadaccomplished when, in 1981, he retired early at age 60 from King’s College London to start a new life at Bar-Ilan University in Israel. His first steps on this path were taken in the Spring of 1954when(againsttheadviceofhisCambridgeUniversitycolleagues!)CyrilDombthen 32yearsold,appliedforthepositionofProfessorofTheoreticalPhysicsatKing’sCollege London. This Chair had been established in 1947 soon after the College returned to its original London home in Somerset House on the banks of the River Thames at the end of World War II following its evacuation to Bristol during the war. The College had been founded in 1829 by the “Establishment” as a counterblast to that “Godless hole in Gower Street,” namely,UniversityCollege,and,accordingly,byStatuteaFacultyofTheologywastoplay aprominentrole. ThedoorsoftheFacultyofNaturalScienceopenedatKing’sin1831.Butinthosedays “TheoreticalPhysics”wasnotyetthenameofanyacceptedscientificfield.Ratheraposition of“ProfessorofNaturalPhilosophy”wasestablishedand,in1860,JamesClerkMaxwell wassonamed!Indeed,asmanyyearslaterCyrilDombwastoestablishbyhisownoriginal historicalresearches,itwasduringthesubsequentyearsatKing’sthatMaxwelldidmuch of his major work. Maxwell chose to resign in 1868 and return to his Glenlair estate in Scotlandbefore,threeyearslater,onceagainmovingsouthtobecomeCavendishProfessor atCambridge. However,aDepartmentofPhysics,assuch,wasopenedatKing’sin1834,theexception- allyversatileexperimentalist,CharlesWheatstone,becomingthefirstProfessorofPhysics. Laterthetwodepartmentsmergedanddistinguishedscientistsacceptedappointments,three ofwhom,CharlesBarkla,OwenRichardson,andEdwardAppleton,laterreceivedtheNobel Prize. When theCollegereturned toLondonin1946,JohnTurton Randallwasappointed (cid:2) M.E.Fisher( ) InstituteforPhysicalScienceandTechnology,UniversityofMaryland,CollegePark,MD20742,USA e-mail:[email protected] CyrilDomb:APersonalViewandAppreciation 511 WheatstoneProfessorandHeadofDepartment.Hewasalreadywellknownastheinventor (with H.A. Boot) of the cavity magnetron—the crucial “heart of radar” that protected the BritishIslesthroughtheWar. Randall, as Cyril Domb later noted, was a superb scientific administrator. Without a doubthehadastronghandinappointingthefirstProfessorofTheoreticalPhysics,namely, CharlesCoulsoninternationallyrenownedasatheoreticalquantumchemist.Indeed,Ran- dallhaddecidedtofocustheDepartmentincreasinglyonproblemsinBiophysics—aplan thatadecadelateruncoveredatKing’sthedouble-helixstructureofDNAthroughtheexper- imentallaborsofMauriceWilkins,hisstudentRaymondGoslingand,especially,Rosalind Franklin.Butatthepersonallevelforme,asanundergraduateinPhysics,Coulsonwasjust mytutorinbasicquantummechanics.However,hewasalsoalayMethodistpreacherand encouragedTheologystudentsatKing’s.Amusementwasgeneratedinhisresearchgroup bytheperhapsapocryphalletteraddressedtohimas:“ProfessorofTheologicalPhysics!” In 1952, while I was away from King’s serving for two years in the Royal Air Force, CoulsonleftforaChairofMathematicsinOxfordandwassucceededbyanotherprominent theoretical chemist, H. Christopher Longuet-Higgins. Christopher was an excellent musi- cianandaninteractiveindividual.Itwasnotedbysomethat:“InkeepingwiththeCollege’s religious foundation, he is the son of a parson even if he himself has turned out to be a nonbeliever.”ButinonlytwoyearsLonguet-HigginsmovedtotheChemistryDepartment atCambridgewhere,increasinglydisenchantedbythepredominantroleofbrute-forcecom- putationintheoreticalchemistry—withlittlethoughtashesawit—hesoonshiftedhisin- tereststotheworkingsofthebrain.Tothatend,indeed,heeventuallyleftCambridgefirst forEdinburghandthentoSussex. Thiswasthesettingwhen,inthespringof1954,CyrilDomb,backinCambridgesince 1952asaLecturer,consideredtheadvertisementfortheopenChairatLondonand,ashe has related [1–3], looked carefully into the activities in Physics at King’s and decided to apply.Anotherprominent,computationallyorientedchemisthadvisitedthatspringandleft asomewhatsourimpressiononmembersofLonguet-Higgins’groupwithwhich,ashalf- experimentalist and half-theoretician [4], I was informally but closely associated. It was, thus, pleasant to learn a few months later that, likely under Randall’s guiding hand, the successortoLonguet-HigginswastobeanexpertinthefieldofStatisticalPhysics. In fact, having applied, Cyril was soon short-listed and invited for interview. We now know that Cyril’s first mentor from his war-time service, M.H.L. (Maurice) Pryce, was present at the interview for the Chair as an external advisor to the University of London [1–3]. Because of his previous association with Cyril he abstained from asking any ques- tions.However,whentheinterviewswiththefourcandidateswerecompleteandthechoice oftheSelectionCommitteewasclearlyconvergingonDr.CyrilDomb,PrycetoldtheKing’s representativesthatthiscandidatewasofOrthodoxJewishfaithandwouldbeunabletolec- tureorattendCollegefunctionsaftersundownonFridaysoronthemajorJewishholidays. But the immediate response of Peter Noble, the Principal of King’s College who chaired theSelectionCommitteewas:“AslongasIamPrincipalofthisCollege,therewillbeno religiousdiscrimination”[2].Soitwasthatin1954CyrilDombjoinedKing’sCollegein time for the Michaelmas Term—named, by tradition, for the feast of St. Michael held on 29September. In due course when the Physics Department got to know Cyril Domb as the new Pro- fessorofTheoreticalPhysics,itwasgenerallyappreciatedthathewasofJewishfaithand, furthermore,observant.But,indistinctiontoCoulson’sChristianity,thiswasneveranissue thataroseinthelifeoftheCollege.Nevertheless,somewryobserversremarkedthat:“This 512 M.E.Fisher appointmentisstillinkeepingwiththeCollege’sreligioustraditionsalthoughtheAuthor- ities have now recognized that a scholar who at least respects the Old Testament is to be preferredtoanonbeliever!” The newly minted “Professor Domb” brought many positive characteristics to King’s; butanunusuallysharpawarenessandsensitivitytotheroleof“real”mathematicsinappli- cationstothephysicalsciencesprovedofprimesignificance.Cyril’sundergraduatetraining inMathematicsatPembrokeCollege,Cambridgestartedin1938,theyearofthe“Munich crisis” that preceded World War II. Three years later, he graduated as a “Wrangler”, i.e., with First Class Honours. However, it was his war-time experiences in radar at the Ad- miraltySignalEstablishmentwiththelively-mindedyoungtheorists,HermannBondiand TommyGold,undertheleadershipofFredHoyle,afewyearsolder,thattaughtCyrilthe power of intelligently applied mathematics for practical problems [1]. He also gained an understanding and deep appreciation for probability theory and statistics. Thus, as he has related[1,2],onhisreturntoCambridgeaftertheWarin1946,hedecidedonthefieldof StatisticalMechanicsforhisdoctoralresearches. Soonhediscoveredthatbringingexactmathematicalmethodstobearwasagainreward- ing.FromatalkbyA.R.Milleratthe2VClubinCambridgehelearnedofwhatwenow invariablycall“theIsingModel”andofBethe’sstrikingbutintrinsicallylimitedandapprox- imatetreatment[1].Thence,forhimself,Cyrildiscoveredthetransfermatrixapproachand solvedtheone-dimensionalmodelexactly.But,astheliteraturerevealed,ElliottMontroll, followingthepre-warworkofH.A.KramerswithhispostdoctoralassociateG.H.Wannier, had already been there. Nevertheless, it was through Montroll’s work that Cyril came to learnofOnsager’ssolutionofthetwo-dimensionalmodelinzero-fieldpublishedonlytwo yearspreviouslyin1944. Amajoroutstandingquestionconcernedthebehaviorofthespontaneousmagnetization, M (T).Cyril’sfirststepwastorecognizethatthemannerinwhichM vanishedasT ap- 0 0 proachedthecriticalpoint,T ,entailedanontrivial,nonobviousand,indeedunknowncrit- c icalexponent,latercalledβ.Aswecannowclearlysee,theidentificationoftheexponents asacentralcharacteristicofcriticalbehaviorwas,initself,aboldandsignificantconceptual advance.Andthesuspicionthattheseexponentswere,inlaterterminology“universal”,over wideclassesofmodelssoongrewasCyrilDombandMartinSykes,hislastgraduatestu- dentfromhisthreeyearsinOxfordUniversity,successivelyandreliablelyestimatedfurther basiccriticalexponents[5,6]. SowhatapproachdidCyriltaketofindβ forthetwo-dimensionalIsingmodel?First,in termsofthevariablez=exp(−2J/k T),whichvanisheswhenT →0,heundertookthe B calculationoftheexactexpansioncoefficientsofM (T)toorderz18.Thenin1949[7],from 0 aninsightfulanalysisofthemanyexactcoefficientsandanintelligentasymptoticextrapola- tion,heconcludedthatβwasclosetoorsomewhatlessthan0.16.Onlythreeyearslaterwas itseenhowwellthisgraduatestudenthaddone!Then,viaatour-de-forceexactcalculation by C.N. Yang—which he has described as the hardest in his career—did the exact result, namelyβ=0.125,becomegenerallyknown! Meanwhile, unknown to both Domb and Yang, in unpublished work described in this specialissuebyRodneyBaxter,OnsagerhimselfwithBruriaKaufman,hadindependently foundtheexactexpressionforM (T).Heevenannouncedit,intypicallycrypticfashion,at 0 a1949meetinginFlorencetowhichCyrilDombwasthentoojuniortobeinvited.Never- theless,despiteearlyhopes—andrecurringfalseclaims[8,9]—thethree-dimensionalIsing modelhasresistedmanyattemptstoobtainexactresultsforitscriticalbehavior.But,thanks tothepioneeringinsightsofCyrilDombandthedevelopmentsofthetheoreticaltechniques helaunchedover60yearsago,wecannowbesurethatthevalueofβ fortheIsingmodel CyrilDomb:APersonalViewandAppreciation 513 inthreespatialdimensionsiscloseto0.326[10].Furthermore,withintheprecisionofmany differentstudiesforavarietyofsystems,thisisalsotheverdictofexperiment[11]. For me personally at King’s in 1954, I soon benefited from the evident concern of the “newProfessor”fortheindividualgraduatestudentshehad“inherited”.AsIlatercameto appreciate,thischaracteristicembodiedlessonsgainedfromhisownmentors,maybefirst Fred Hoyle, then as mentioned, M.H.L. Pryce, and at Oxford from 1949, a refugee from NaziGermanybutbythenknighted,SirFrancisSimon,ProfessorofExperimentalPhysics. ThelessonshadgonetoCyril’sheartwheresurelytheyhadfounddeepintrinsicresonances. Thus,sensingmyinterestsinmathematics,Cyriltoldmeofhisinstructivestudyofitera- tiveprocessesforsolvingequations[12]stimulatedbyDouglasHartree—of“Hartree-Fock” fameinquantummechanicsbutalsowellknownforhisnumericalworksonhardproblems. Cyril had noticed “degenerate iterative processes” which, in fact, solved functional equa- tions.Ifoundthismostintriguingandwasdelightedtobeinvitedtoexplorefurther[13].In carryingthemathematicsforwardIlearnedalot—includingthepowerofanalyticcontinua- tionwhich,indeed,Ihadneverpreviouslygrasped!And,beforelong,Cyrilalsointroduced me to what became my life-time affair with random walks and the beauties of generating functions[14]. AmongthedutiesCyrilDombnaturallyassumedatKing’swasarrangingseminarsfor thetheoreticalgroup.Hisstudentsandothersenjoyedthereadyaccesstothevisitorswho spoke. Indeed, I still remember vividly the visit of the third of the six students Cyril had guided to Ph.D.s in Oxford, namely Renfrey Potts, a Rhodes Scholar from Australia. Of course,hewastheoriginatorofthe“PottsModel”,avaluableq-foldextensionoftheIsing modeldevised,indeed,atthesuggestionofhisthesisadvisor[15,16]!Butwhenhevisited King’shespokeofhisworkwithElliottMontrolloncorrelationfunctionsforIsingmodels intwodimensions.Cyclicmatricesappearedinquantity.Andmyeyeswereopenedwhen, in response to my question, he explained that cyclic matrices, however big, were always easytodiagonalize! Cyril’sconcernforthewelfareofthemembershisgroupwasremarkable.Ondiscover- ingthatmysupposedlyprestigiousUniversityofLondonPostgraduateStudentshipactually paid less than the standard Government grants while I already had a wife and child (and worked as a Student Librarian for the Physics Library), he made a special appeal to the CollegePrincipalforsomeadditionalsupport.Thereplythat“Mr.Fishershouldhavecon- sideredhissituationbeforeundertakingtheresponsibilitiesofmatrimonyandpatrimony,” brought no financial relief! But the actions on my behalf that elicited this message were surelyappreciated. Concernfortheongoingwellbeingofhistheoretical“family”extendedalsototheirfu- tureoptions.Iwaspersonallytobenefitwhenthetimecametoaddresstheperennialques- tion: “But what might I do professionally once my Ph.D. thesis is accepted?” Cyril must havehaddoubtsastotheprospectsofanalogcomputationinBritain—albeitelectronicand of“ultrahighspeed”asmythesisworkwithDonaldMacKayentailed[4].Accordingly,he specificallywrotetoDouglasHartreetoaskhisopinionregardingwhatopportunitiesmight be available in the field. The detailed reply was not encouraging: the future in the U.K. seemed to hold no promise at all. In retrospect, the aircraft industry in the United States might have provided openings for me since analog computers coupled ideally well to air- planesystems.ButinthateramyfamilyandIwerenotreadytoemigrate.(Indeed,without regrets,IturnedasideanapproachfromamathematicssectionoftheU.S.NationalBureau of Standards—as it was then named—perhaps stimulated by a theorem on matrices I had advancedthatCyrilhadcommunicatedtotheProceedingsoftheCambridgePhilosophical Society[17].) 514 M.E.Fisher With no future in my chosen field and a family to care for, a change of direction was needed.CyrilfoundafreshproblemintheoryformefromhiscontactswithAharonKatchal- sky(laterKatzir),thedynamicChairofthePolymerDivisionattheWeizmannInstitute.This concernedthebehaviorofpolyelectrolytes;primedwithatask,Iwasputupforandawarded aD.S.I.R.SeniorResearchFellowship.Thatopenedapathformeintostatisticalphysics and,indeed,intophysicalchemistry! Asimilarconcern forhisstudentssoonbroughttoLondon,fromOxford,Cyril’smost effective and long-term collaborator, Martin F. Sykes, who, in, turn, became one of my lifetime’sclosefriends.Martinhadnoevidentacademicambitionsofthestandardgenrebut was deeply devoted to his researches on lattice configurations and their enumeration. His strikingtalentsinthisfieldprovidedperfecttoolsforderivingexactlytheseriesexpansions thatunder-pinnedCyrilDomb’sfundamentaltechniquetoextractcriticalexponentsforso manystatisticalmodels.ForMartin,duringhislongassociationwithKing’s,Cyrilarranged atitleuniqueintheCollegeAnnals,namely:HonoraryDirectorofResearch. Beyond his personal prowess at bringing mathematical concepts to bear on practical problems,Cyril’scuriosityandhisboldnessinnewfields,broughttohisgroupanunceasing paradeoffascinatingnovelproblemscompletewithideasonhowtotacklethem.Withhis Oxford student Hugh Barron, inspired by a polymorphic fcc-to-hcp lattice transition then recentlydiscoveredinsolidheliumbyDugdaleandSimon,hediscussedthecorresponding zero-pointquantum-mechanicaldynamics[18].WithDugdalehelaterwroteaninstructive reviewofsolidheliumanditsphases[19]and,moregenerally,ofthetheoryofmelting[20]. TothisdayIremembermyexcitementandpleasureatlearningCyril’sbasicargumentasto whyameltinglinecannotendinacriticalpoint[19,20]:Simplyput,asolidhaslongrange order,aliquiddoesnot;sowhilethemeltingtransitionmightceasetobeoffirst-order,it cannotceasetoexist.TheessenceofthisargumentappliesequallytoIsingandHeisenberg latticeantiferromagneticspinmodelsinamagneticfield.There,indeed,atricriticalpoint oftenappearsmarkingthetransitionfromtheanalogoffirst-ordermeltingtoacontinuous transition locus or lambda line. Years later, the same phenomenon arose in liquid helium 3–4mixtures. In1958Cyril,newlymarried,tooksevenmonthsleavetoworkwithElliottMontrollin Maryland; meanwhile Martin Sykes and I collaborated fruitfully on excluded volume and relatedlatticeproblems.FromthatvisitCyrilbroughtbackfreshchallenges:thefrequency spectraofcrystallattices,thespecialintegralsinvolved,andtheirbeautifulconnectionsto randomwalks[21].Inanotherenterprise,fromJohnHammersleyandthestatisticscommu- nity,helearnedofthefertileorchardsofpercolationproblems.Thesegavemethepleasure offinding,withmygraduatestudentJohnW.Essam,exactsolutionsforBethelattices[22]. Such“lattices”were,ofcourse,Cyril’sinsightfulabstractionofthesenseinwhichBethe’s 1935approximation—throughwhichCyrilwasfirstledtoIsingmodels—could,infact,be regardedasprovidingexactsolutionsforaspecial,butnontrivial,classofinfinite,lattice- like statistical systems. The article with Essam [22] started: “Recently Domb1 has drawn attention to the problem of determining the distribution of cluster sizes for particles dis- tributed ...”; and Footnote 1 referred to a talk by Cyril at a March 1959 Conference at BirkbeckCollegeandareportinNature184,509(1959). Asamatterofprinciple,soitseemed,the“Professor”assignedquitedistinctproblems to the individual thesis students in his group. But he was pleased to have the members learn from one another even when, as in the work of his first graduate student at King’s, JohnZucker—happily,acontributortothisspecialissue—mypersonalinterestledtowhat mightbeviewedas“destructiveconsequences.”ByapplyingCyril’sapproachoftakingthe mathematicsseriously,wediscovered[23]thataseductiveandboldideaforcapturingthe CyrilDomb:APersonalViewandAppreciation 515 mainconsequencesofstronginteractions andsubsequentnonlinearities inquantal ground statesforcrystalswastotallywithoutrealmerit! Butinothercasestheoutcomeswerefarhappierand,needlesstosay,wonCyril’sstrong support. With the increasing availability of (digital!) computational facilities, he had sug- gestedtoJillBonnerthatsheexaminewhatmightbedonenumericallytostudyHeisenberg model spin 1/2 linear chains with nearest-neighbor couplings. The initial results intrigued meandaclosecollaborationwithJilldevelopedwhich,infact,eventuallyledtooneofmy most-highlycited papers [24].Italso,generated auniquesurprise!Itshouldbeexplained that in 1963–1964 I was on leave at the Rockefeller University with Mark Kac thanks to CyrilDombwhohadearlierrecommendedmewarmlytoElliottMontroll(bythenworking attheIBMT.J.WatsonResearchCenterinYorktownHeights). JillandIhadsubmittedourarticletoThePhysicalReviewwhen,oneday,therecamein themailtoRockefellerarejectionletterfromajournalofwhichIhadneverheardandto whichwehadneversentthepaper.Thenottoo-discouragingcommunicationwassignedby Phil(P.W.)Anderson—alreadyWorldfamousforhismanyoriginalanddeepperspectives oncondensedmatterphysics.Itinformedusthatourworkwas“judgedunsuitable”forhis journal because it was felt to be primarily of “archival interest.” So what had happened? First,Andersonwasinitiatinganaimed-to-be-prestigiousinternationaljournaltitledsimply “Physics.” Second, Anderson had visited Cyril Domb at King’s and asked what novel re- searchesmightbeworthyofpublicationinthisnewvenue.Evermindfulofthemeritsand interestsofhisassociates,youngorold,Cyrilhadrecommendedourworkand,further,had givenAndersona“preprint”ofourarticle. MyyearonleaveintheStateswithmyfamilyengenderedsometemptingoffersand,in duecourse,havingreturnedtoKing’s,nowatfullprofessorialrank,thanksagaintoCyril’s support,wedecidedtogiveCornellUniversityatry.ThusIresignedfromKing’sinmid- summer1966.Theplanwastogofora“fewyears”whicheventuallybecameover20! Naturally, my close scientific ties with Cyril Domb diminished over the years while I watched his group grow further in international esteem. Series expansion techniques had beentakenupactivelyintheUnitedStatesbyGeneStanleyatM.I.T.andMichaelWortis andhisstudentDavidJasnowinIllinois.Distinguishedvisitorsfromoverseashadbeenat- tractedtoKing’sbeforeIleft—IrecallespeciallyGeorgeA.BakerJr.,fromLosAlamosand Brookhaven,andJohnF.NagleafterhisPh.D.atYalewithOnsager.Andothersfollowed: DouglasBettsfromCanadaand,notably,fromAustralia,TonyGuttman,theEditorofthis specialissue.ThevisitorsbroughtnewskillsandideastoKing’sandinturnbenefitedfrom thestimulatingresearchenvironment. PersonalhonorsshouldhavebeenflowingtoCyrilDombinthe1960’s.But,alas,since life in any field of endeavor is seldom completely just, formal recognition came unduly slowly.In1977,thankstothethoughtfulinitiativeofSamEdwards,thebrilliantandversa- tileCambridgetheorist(whohad,also,encouragedmeatanearlystage),Cyrilwaselected aFellowoftheRoyalSociety,newswelcomedbyallhiscolleagues,students,andadmirers. In turn, Cyril was warmed by the many letters of congratulation, especially one from Sir NevilleMott,thenCavendishProfessoratCambridge,whoexpressedhisfailuretounder- standthedelayedelection.However,havingsignedhisnameinthesamegreatCharter-Book whereIsaacNewtonhadsignedin1671,JamesClerkMaxwellin1861,andMaxBornin 1939,Cyrilwentontoorganizeaspecialexhibitionforthe1979AnnualConversazioneof the Royal Society. This commemorated the centenary of Maxwell’s death and, no doubt, therolethatKing’sCollegeLondonhadplayedinMaxwell’sownscientificlifewaswell featured. Also in 1979 Cyril received an Honorary Doctorate from Yeshiva University in New YorkCity,thefirstacademichomeofJoelLebowitz.ThentheMaxBornMedalfor1981 516 M.E.Fisher wasawardedtoCyriljointlybytheGermanPhysicalSocietyandbytheBritishInstituteof Physics.ThecitationappropriatelyidentifiedthepioneeringresearchesofCyrilDomband theschoolhehadfoundedatKing’sCollegeasprovidingthefertilesoilfromwhichgrew, first, detailed scaling theories and thence, in the hands of Kenneth Wilson, the powerful renormalizationgroupapproach. Asobservedaboveintheintroductoryparagraph,1981wasalsotheyearinwhichCyril retiredearlyfromKing’sandmovedwithhisfamilytoIsrael,livinginJerusalembutcom- mutingtoBarIlanUniversity.There,verysoon,hispositiveinfluenceandhisconcernfor colleagues and students became evident. It is good to see that articles from two of them, ShlomoHavlinandIdoKanter,appearinthisspecialissue. At Bar Ilan, Cyril also took the opportunity to look back in historical breadth on the fieldofcriticalphenomenawhich,inmanyways,hadbeensparkedbyhisfamousreviewof 1960publishedinAdvancesinPhysics[25]:theresultin1996washismasterlybookThe CriticalPoint.TheForeword,whichitwasmypersonalpleasuretocontribute[26],describes Cyril’sgreatservicetotheInternationalStatisticalPhysicsCommunityininitiatingwithMel Greenthefamousseriesofauthoritativearticles[27,28]usuallyknownsimplyas“Domb andGreen.”Thefirstvolumeappearedin1972.Afterfivefurthervolumes,verysadly,Mel Green died in Philadelphia; but Cyril then enlisted Joel Lebowitz to help carry the series through to its final close in 2001 with Vol. 20 containing a cumulative index of Authors, Titles, Subjects and Contents. On my book shelves, it now occupies over a half-a-meter filled with treasures of basic science. What a magnificent memorial for a life devoted to scholarshipanddeeplyvaluedtraditions! References 1. Domb,C.:Somereminiscencesaboutmyearlycareer.PhysicaA168,1–21(1990) 2. Domb,C.:Reminiscences,pp.1–204.DocostoryLtd.,Raanana,Israel(2007) 3. Schweber,S.S.:AninterviewwithProf.CyrilDombinJerusalemon10June2002.Availableonlineat: http://www.authors.library.caltech.edu/5456/1/hrst.mit.edu/hrs/renormalization/Domb/ 4. Fisher,M.E.:Thesolutionofproblemsintheoreticalphysicsbyelectronicanaloguemethods.Ph.D. thesis,UniversityofLondon(January1957) 5. Domb,C.,Sykes,M.F.:UseofseriesexpansionsfortheIsingmodelsusceptibilityandexcludedvolume problem.J.Math.Phys.2,63–67(1961) 6. Domb,C.,Sykes,M.F.:EffectofchangeofspinonthecriticalpropertiesoftheIsingandHeisenberg models.Phys.Rev.128,168–173(1962) 7. Domb, C.: Order-disorder statistics II. A two-dimensional model. Proc. Roy. Soc. A 199, 199–221 (1949) 8. Wu,F.Y.,McCoy,B.M.,Fisher,M.E.,Chayes,L.:Commentonarecentconjecturedsolutionofthe three-dimensionalIsingmodel.Philos.Mag.88,3093–3095(2008) 9. Wu,F.Y.,McCoy,B.M.,Fisher,M.E.,Chayes,L.:Rejoindertotheresponse.Philos.Mag.88,3103 (2008).Philos.Mag.89,195(2009).Erratum 10. Pelissetto,A.,Vicari,E.:Criticalphenomenaandrenormalization-grouptheory.Phys.Rep.368,549– 727(2002) 11. Sengers,J.V.,Shanks,J.G.:Experimentalcritical-exponentvaluesinfluids.J.Stat.Phys.137,857–877 (2009) 12. Domb,C.:Oniterativesolutionsofalgebraicequations.Proc.Camb.Philos.Soc.45,237–240(1949) 13. Domb,C.,Fisher,M.E.:Oniterativeprocessesandfunctionalequations.Proc.Camb.Philos.Soc.52, 652–662(1956) 14. Domb,C.,Fisher,M.E.:Onrandomwalkswithrestrictedreversals.Proc.Camb.Philos.Soc.54,48–59 (1958) 15. Potts,R.B.:Somegeneralizedorder-disorder transformations. Proc.Camb.Philos.Soc.48,106–109 (1952) 16. Domb,C.:ConfigurationalstudiesofPottsmodels.J.Phys.A,Math.Gen.7,1335–1348(1974) CyrilDomb:APersonalViewandAppreciation 517 17. Fisher,M.E.,Fuller,A.T.:Onthestabilizationofmatricesandtheconvergenceoflineariterativepro- cesses.Proc.Camb.Philos.Soc.54,417–425(1958) 18. Barron,T.H.K.,Domb,C.:Onthecubicandhexagonalclose-packedlattices.Proc.Roy.Soc.A227, 447–465(1955) 19. Domb, C., Dugdale, J.S.: Solid helium. In: Gorter, C.J. (ed.) Progress in Low Temperature Physics, pp.338–367.North-Holland,Amsterdam(1957).Chap.XI 20. Domb,C.:Sometheoreticalaspectsofmelting.NuovoCimento9(1),9–26(1958) 21. Domb,C.,Maradudin,A.A.,Montroll,E.W.,Weiss,G.H.:Vibrationfrequencyspectraofdisordered latticesI.Momentsofthespectrafordisorderedlinearchains.Phys.Rev.115,18–24(1959) 22. Fisher,M.E.,Essam,J.W.:Someclustersizeandpercolationproblems.J.Math.Phys.2,609–619(1961) 23. Fisher,M.E.,Zucker,I.J.:Onanon-lineardifferentialequationforthezero-pointenergiesoftheraregas solids.Proc.Camb.Philos.Soc.57,107–114(1961) 24. Bonner,J.C.,Fisher,M.E.:Linearmagneticchainswithanisotropiccoupling.Phys.Rev.135,A640– A658(1964) 25. Domb,C.:Onthetheoryofcooperativephenomena.Adv.Phys.Philos.Mag.Suppl.9,149–361(1960) 26. Fisher,M.E.:Foreword:abouttheauthorandthesubject.In:Domb,C.,TheCriticalPoint:AHistorical IntroductiontotheModernTheoryofCriticalPhenomena,pp.xiii–xviii.TaylorandFrancis,London (1996) 27. Domb,C.,Green,M.S.(eds.):PhaseTransitionsandCriticalPhenomena,vols.1,2,3,4(unpublished), 5A,5B,and6.AcademicPress,London(1972–1976) 28. Domb,C.,Lebowitz,J.L.(eds.):PhaseTransitionsandCriticalPhenomena,vols.7–20.AcademicPress, London(1983–2001)