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1、EurophysicsLettersPREPRINTAgeingindisorderedmagnetsandlocalscale-invarianceMalteHenkel1,2andMichelPleimling3,41LaboratoiredePhysiquedesMat´eriaux(CNRSUMR7556),Universit´eHenriPoincar´eNancyI,B.P.239,F–54506Vandœuvrel`esNancyCedex,France2DipartimentodiFisic
2、a/INFN-SezionediFirenze,Universit`adiFirenze,I-50019SestoFiorentino,Italy3Institutf¨urTheoretischePhysikI,Universit¨atErlangen-N¨urnberg,D–91058Erlangen,Germany4DepartmentofPhysics,VirginiaPolytechnicInstituteandStateUniversity,Blacksburg,VA24061-0435,USAP
3、ACS.05.70.Ln–Nonequilibriumandirreversiblethermodynamics.PACS.64.60.Ht–Dynamiccriticalphenomena.PACS.75.10.Nr–Spin-glassandotherrandommodels.Abstract.–Theageingofthebond-disorderedtwo-dimensionalIsingmodelquenchedtobelowitscriticalpointisstudiedthroughthet
4、wo-timeautocorrelatorandthermoremanentmagnetization(trm).Thecorrespondingageingexponentsaredetermined.Theformofthescalingfunctionofthetrmiswelldescribedbythetheoryoflocalscale-invariance.AspinsystemquenchedtobeloworexactlyatitscriticaltemperatureTcundergoe
5、sageing,thatistime-translationinvarianceisbrokenandobservablessuchascorrelationorresponsefunctionsdisplaydynamicalscaling.Whilesystematicstudiesofageingappeartohavebeencarriedoutfirstinstudiesofthemechanicalresponseofglassysystems[1],ithasbeenrealizedrelati
6、velyrecentlythatasimilarphenomenologyalsoappliesforsimpleferro-magnetswithoutdisorder,see[2–5]forreviews.Inthesesimplersystems,forbothT=TcandT7、iththetypicallinearsizeofcorre-latedororderedclusters,respectively.Itiscommontostudyageingthroughthetwo-timeautocorrelationfunctionC(t,s)=hφ(t,r)φ(s,r)iorthetwo-timelinearautoresponsefunc-tionR(t,s)=δhφ(t,r)i/δh(s,r)
8、h=0.Hereφ(t,r)denotesthespace-time-depe
9、ndentorder-parameter,h(s,r)isthespace-time-dependentconjugatemagneticfield,tisreferredtoasobservationtimeandsaswaitingtime.Forageingsystems,averagesdependonbothtandsandnotmerelyonthedifferenceτ=t−s.Intheageingr