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页数:31页
时间:2019-05-27
《First steps of a nucleation theory in disordered systems》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、FirststepsofanucleationtheoryindisorderedsystemsSilvioFranzTheAbdusSalamInternationalCenterforTheoreticalPhysicsStradaCostiera11,P.O.Box563,I-34100Trieste(Italy)E-mail:franz@ictp.trieste.itFebruary2,2008AbstractWedeviseafieldtheoreticalformalismforamicroscopictheoryofnucleationprocessesandp
2、hasecoexistenceinfinitedimensionalglassysystems.Westudydisorderedp-spinmodelswithlargebutfiniterangeofinteraction.Weworkintheframeworkofglassyeffectivepotentialtheorywhichinmean-fieldisanon-convex,twominimafunctionoftheoverlap.Weassociatemetastabilityandphasecoexistencewiththeexistenceofspacei
3、nhomogeneoussolutionsofsuitablefieldequationsandwestudythesimplestofsuchsolutions.1IntroductionAprominenttheoreticalprobleminthephysicsofglassysystemsisthecom-arXiv:cond-mat/0412383v2[cond-mat.stat-mech]23Feb2005prehensionoftheprocessesthatrestoreergodicityinregionswhereapprox-imatedliquidt
4、heoriesorMean-Fieldmodelspredictaspuriousstructuralarrest.ItiswellknownthattheModeCouplingTheory[1],whiledescribingcorrectlyseveralaspectsofthedynamicsofmoderatelysupercooledliquids,1predictsthedivergenceoftherelaxationtimeandergodicitybreakingatatemperatureTcwellabovetheobservedlaboratory
5、glasstransitiontemper-atureTG.Inthesocalled“randomfirstorderphasetransitionscenario”[2],correspondingto“onestepreplicasymmetrybreaking”(1RSB)[3]inmeanfielddisorderedmodels,thisergodicitybreakingappearstoberelatedtotheappearanceofexponentiallynumerousmetastablestates,capabletotrapthesysteminr
6、egionsoffree-energyextensivelyhigherthanthethermo-dynamicvalue.WithinthisscenarioaKauzmann-likeentropycrisisoccursatatemperatureTK7、disappearassoonasthefiniterangecharac-terofinteractionisproperlytreated.Aremarkablehypothesisstatesthatwhileacquiringafinitelifetime,thegrossstructureofmetastablestatessurvivesinshortrangeglassysystemsanddominatesthelowtemperaturerelaxation.Unfortunately,amicros
7、disappearassoonasthefiniterangecharac-terofinteractionisproperlytreated.Aremarkablehypothesisstatesthatwhileacquiringafinitelifetime,thegrossstructureofmetastablestatessurvivesinshortrangeglassysystemsanddominatesthelowtemperaturerelaxation.Unfortunately,amicros
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