the mass gap of the nonlinear sigma model through the finite temperature effective actionnew

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1、TheMassGapoftheNonlinearσModelthroughtheFiniteTemperatureEffectiveActionDavidS´en´echalCentredeRechercheenPhysiqueduSolideetD´epartementdePhysique,Universit´edeSherbrooke,Sherbrooke,Qu´ebec,CanadaJ1K2R1.(November1992)AbstractTheO(3)nonlinearσmodelisstudiedinthedisor

2、deredphase,usingthetechniquesoftheeffectiveactionandfinitetemperaturefieldtheory.ThenonlinearconstraintisimplementedthroughaLagrangemultiplier.Thefinitetemperatureeffectivepotentialforthismultiplieriscalculatedatoneloop.Theexistenceofanontrivialminimumforthispotentialis

3、thesignalofadisorderedphaseinwhichthelowestexcitedstateisamassivetriplet.Themassgapiseasilycalculatedasafunctionoftemperatureindimensions1,2and3.Indimension1,thisgapisknownastheHaldanegap,anditstemperaturedependenceiscomparedwithexperimentalresults.arXiv:cond-mat/9

4、212001v29Dec199275.10.Jm,11.10.LmTypesetusingREVTEX1TheO(3)nonlinearσmodel(NLσ)offersagooddescriptionofquantumantiferromag-netsatlongwavelengths,assuggestedbyrenormalizationgroupanalyses1.ThemappingbetweenthenonlinearσmodelandtheHeisenbergmodelwasfirstestablishedbyHa

5、ldane2,whoalsoarguedthatatopologicalHopftermshouldbepresentinthecaseofhalf-integerspinsinonedimension3(thisdistinctionbetweenhalf-integerandintegerspinsdisappearsintwodimensions).Forintegerspins,inwhichcasetheHopftermisabsent,Haldanear-guedthatthelowestexcitationss

6、houldexhibitamassgap.Accordingly,theseexcitations(themagnons)arenolongerGoldstonemodesandtherotationsymmetryofthespinsisnolongerspontaneouslybroken:thesymmetryhasbeendynamicallyrestoredbyquantumfluc-tuations.Thisphenomenonhasfoundanexperimentalrealizationinquasione-

7、dimensionalantiferromagnetsintheirdisorderedphase4.Inthispaperwecalculatethetemperaturedependenceofthismassgapindimensions1to3withintheframeworkofthefinitetemperatureeffectiveactionofthenonlinearσmodel.TheuseofthistechniqueisfacilitatedbytheLorentzinvarianceoftheNLσm

8、odel,whichensuresthatthemagnonspeedisnotaffectedbyquantumcorrections.TheO(3)nonlinearσmodeldescribesthedynamicsofaunitvector~ϕrepresentingthelocal