Numerical evidence of the spin-chirality decoupling in the t

Ordering of the three-dimensional Heisenberg spin glass with Gaussian coupling is studied by extensive Monte Carlo simulations. The model undergoes successive chiral-glass and spin-glass transitions at nonzero temperatures T_{CG} > T_{SG} > 0, exhibiting t

Numericalevidenceofthespin-chiralitydecouplinginthethree-dimensional

Heisenbergspinglass

DaoXuanVietandHikaruKawamura

DepartmentofEarthandSpaceScience,FacultyofScience,OsakaUniversity,Toyonaka560-0043,Japan

(Dated:August25,2008)

Orderingofthethree-dimensionalHeisenbergspinglasswithGaussiancouplingisstudiedbyextensiveMonteCarlosimulations.Themodelundergoessuccessivechiral-glassandspin-glasstransitionsatnonzerotemperaturesTCG>TSG>0,exhibitingthespin-chiralitydecoupling.

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00PACSnumbers:

2 gTheissueofthespin-glass(SG)orderinghasbeenustudiedquiteextensivelyforyears,andcontinuedtogiveAanimpactonsurroundingareas.Meanwhile,theorigi- 5nalproblemofthemagneticorderingoftypicalspin-glass2magnetse.g.,canonicalSG,stillremainstobeelusive AsmagneticinteractionsinmanySGmaterialsarenearly]nisotropic,itisimportanttoelucidatetheorderingprop-nertiesofthethree-dimensional(3D)isotropicHeisenberg-SG.Althoughearliernumericalstudiessuggestedthatsithe3DHeisenbergSGexhibitedonlyaT=0transitiond3],oneofthepresentauthors(H.K.)suggestedthat.tthemodelmightexhibita nite-temperaturetransitionainitschiralsector[4].Chiralityisamultispinvariablemrepresentingthehandednessofthenoncollinearornon--dcoplanarstructuresinducedbyfrustration.Ithassub-nsequentlybeensuggestedthat,intheorderingofthe3DHeisenbergSG,thechiralitywas“decoupled”fromthecospin,thechiral-glass(CG)ordertakingplaceatatem-[ peraturehigherthantheSGorder,TCG>TSG[5,6,7]. 1Basedonsuchaspin-chiralitydecouplingpictureofthe3DisotropicHeisenbergSG,achiralityscenarioofexper-8vimentalSGtransitionwasproposed7]:Accordingto2thisscenario,thechiralityisahiddenorderparameterof3SGtransition.RealSGtransitionofweaklyanisotropic3.SGmagnetsisthena“disguised”CGtransition,where8thechiralityismixedintothespinsectorviaaweakran-0dommagneticanisotropy.

80Althoughconsensusnowseemstoappearinrecentnu-:vmericalstudiesthatthe3DHeisenbergSGindeedex-ihibitsa nite-temperaturetransitionX11],thenatureofthetransition,especiallywhetherthermodelreallyexhibitsthespin-chiralitydecoupling,isstillaunderhotdebate.Obviously,itiscruciallyimportanttoclarifytheorderingofthe3DHeisenbergSGmodel.Thepresentsituation,however,isnotcompletelysatis-factory.Mentioningsomeoftherecentnumericalworks:BysimulatingthemodelofmodestlatticesizesL≤20(Lbeingthelineardimension)butwithrathersmallnumberofsamplesofNs=32(fortheirlargestL),HukushimaandKawamurapresentedsupportforthespin-chiralitydecouplingBycontrast,LeeandYoungclaimedonthebasisoftheirdataofthecorrelation-lengthratiosξ/Lthatthespinandthechiralityorderatacommontem-perature,thusnospin-chiralitydecoupling[9,11].Theirdata,however,su ersfromeithersmalllatticesizesof

onlyL≤12orsmallnumberofsamplesofNs=56[11].CamposetalsimulatedthesamemodeltomuchlargerlatticesL=32withlargerofsamplesNs=1,000,butnodatabelowTg[10].Camposetalclaimedthatthechiralandspinsectorsundergosimulta-neouslyaKosterlitz-Thouless(KT)transitionwithmas-sivelogarithmiccorrections.Thisinterpretation,how-ever,wascriticizedinRef.[12].

Undersuchcircumstances,weperformherealarge-scaleMonteCarlosimulationofthe3DHeisenbergSGinordertoshedfurtherlightonthenatureofitsspinandchiralityordering.Weexceedtheprevioussimula-tionsbysimulatingthesystemaslargeasL=32totemperaturesconsiderablylowerthanTgforlargenum-berofsamplesoforderNs 103.Notethatnoneoftheprevioussimulationssatis edallthesecriteriasimulta-neously.Moreimportantly,wecalculateseveralindepen-dentphysicalquantitiesincludingthecorrelation-lengthratios,theBinderratiosandtheglassorderparameters,tryingtodrawconsistenttheseindependentquantities,whereasRefs.[9,10,11]concentratedalmostexclusivelyonthecorrelation-lengthratio.Oursimula-tionthenenabledustoconcludethattheSGtransitionoccursatanonzerotemperaturewhichislocatedabout15%belowtheCGtransitiontemperature.Thus,the3DHeisenbergSGcertainlyexhibitsthespin-chiralitydecoupling.

ThemodelistheisotropicclassicalHeisenbergmodelona3Dsimplecubiclatticewiththenearest-neighborGaussiancoupling.TheHamiltonianisgivenby

H=

JijS

i·S j,(1)<ij>

whereS i=(Sx,Storatthei-theiy,Sz)isathree-componentunitvec-site,i

andithe<ij>sumistakenovernearest-neighborpairs.ThecouplingJijarerandomGaussianvariableswithzeromeanandthevarianceJ2.Thelocalchiralityatthei-thsiteandintheµ-thdirec-tionχiµmaybede nedforthreeneighboringHeisenbergspinsbythescalar

χiµ=S i+ eµ·(S i×S i e

µ),(2)

wheree µ(µ=x,y,z)denotesaunitvectoralongthe

µ-thaxis.Thereareintotal3Nlocalchiralvariables.

Ordering of the three-dimensional Heisenberg spin glass with Gaussian coupling is studied by extensive Monte Carlo simulations. The model undergoes successive chiral-glass and spin-glass transitions at nonzero temperatures T_{CG} > T_{SG} > 0, exhibiting t

2

ThelatticecontainsN=L3siteswithL=6,8,12,16,24,32withperiodicboundaryconditions.Sampleav-erageistakenover2000(L=6,8,12),1000(L=16,24)and800(L=32)bondrealizations.Tofacilitatee -cientthermalization,weemploythesingle-spin- ipheat-bathandover-relaxationmethod[10],combinedwiththetemperature-exchangetechnique.Over-relaxationsweepisrepeatedLtimespereveryheat-bathsweep.

Careistakentomakesurethatthesystemisfullyequilibrated.Equilibrationischeckedbythefollowingprocedures.First,wemonitorthesystemtotravelbackandforthmanytimesalongthetemperatureaxisduringthetemperature-exchangeprocess(typicallymorethan10times)betweenthemaximumandminimumtemper-atures,whilewealsocheckthattherelaxationduetothesingle-spin- ipupdatingisfastenoughatthehigh-esttemperature.Thisguaranteesthatdi erentpartsofthephasespacearesampledineach“cycle”ofthetemperature-exch …… 此处隐藏：12629字，全部文档内容请下载后查看。喜欢就下载吧 ……