VOLUME85, NUMBER 4 PHYSICAL REVIEW LETTERS 24JULY2000Stripe Glasses: Self-Generated Randomness in a Uniformly Frustrated SystemJörg Schmalian1and Peter G. Wolynes21Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, Iowa 500112Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801(Received 15 March 2000)We show that a system with competing interactions on different length scales, relevant to the formationof stripes in doped Mott insulators, undergoes a self-generated glass transition which is caused by thefrustrated nature of the interactions and not related to the presence of quenched disorder. An exponen-tially large number of metastable configurations is found, leading to a slow, landscape dominated longtime relaxation and a breakup of the system into a disordered inhomogeneous state.PACS numbers: 75.10.Nr, 61.43.Gt, 74.25.–qCompeting interactions on different length scales areable to stabilize mesoscale phase separations and thecreation of spatial inhomogeneities in a wide variety ofsystems. Examples are stripe formation in doped Mottinsulators, as found in transition metal oxides (TMO)[1,2], domains in magnetic multilayer compounds [3,4],or mesoscopic structures formed by assembling polymersin solution and amphiphiles in water-oil mixtures [5,6].In many of these cases the tendency towards a perfectlyordered array of domains, stripes, etc. is undermined byfrustrating long range interactions [7]. Very often, theseassemblies exhibit a long time dynamics similar to therelaxation seen in glasses. In the context of stripes it hasbeen argued that the presence of only very few quenchedimpurities might already cause a strictly disordered glassystate [8]. Furthermore, recent molecular dynamics calcu-lations for charge ordering in TMO found an anomalouslong time relaxation with a power spectrum similar to1兾f noise [9]. Indeed, there is experimental evidencefor the formation of intrinsic inhomogeneities and even astripe glass in high temperature superconductors and othertransition metal oxides [10–17]. In particular slow, acti-vated dynamics as observed in NMR experiments [13,15]exhibits a striking universality, rather independent of thedetails of added impurities, etc. It is therefore tempting tospeculate that glassiness in these systems is self-generatedand does not rely on the presence of quenched disorder,which may of course further stabilize a glassy state.In this paper we show that the competition of interac-tions on different length scales in a uniformly frustratedsystem exhibits a self-generated glass transition due to theemergence of an exponentially large number of metastablestates. This result is obtained by using the replica approachof Refs. [18,19] and by solving the corresponding manybody problem using the self-consistent screening approxi-mation [20,21]. Since only very few examples exist formodels which exhibit self-generated glassiness [22,23], allthese approaches are extremely important for a better un-derstanding of glassiness in general. Even though our find-ings apply to a broader class of problems than stripes inTMO, we will adopt a language which is specific to thatproblem [24].A model for a uniformly frustrated system with compe-tition on different length scales is given by the Hamilton-ian [7]H 苷12Zd3xΩr0w共x兲21 关=w共x兲兴21u2w共x兲4æ1Q2Zd3xZd3x0w共x兲w共x0兲jx 2 x0j. (1)Here, w共x兲 characterizes charge degrees of freedom, withw共x兲 . 0 in a hole-rich region, w共x兲 , 0 in a hole-poor region, and w共x兲 苷 0 if the local density equalsthe averaged one. If r0, 0 the system tends to phaseseparate since we have to guarantee charge neutrality,具w典 苷 0. The coupling constant, Q, is a measure for thestrength of the Coulomb interaction and characterizes thecompetition between short and long range interactions. Inthe case of strongly anisotropic, quasi–two-dimensionalcuprate superconductors one expects an anisotropy of thegradient term in Eq. (1), which we neglect for simplicity.Despite the absence of a clean derivation of Eq. (1) fromthe many electron Schrödinger equation, we note that itdescribes, on a phenomenological level, many of the majorcompeting effects which yield in microscopic theories arich phase diagram of inhomogeneous spin and chargestructures [25]. For Q 苷 0 and r0, 0 we expect at lowtemperatures long range ordered charge modulations. Asshown in Ref. [26], the Coulomb interaction suppressesthis ordered state for all Q . 0 and finite T . Instead, thesystem undergoes several crossovers. Most interestingly,at low temperatures, where jr共T兲j , 2pQ, a mean fieldanalysis of Eq. (1) shows that besides a correlationlength, j 苷 2共r 1 2pQ 兲21兾2, an additional length scale,lm苷 4p共2pQ 2 r兲21兾2, emerges, which characterizesthe spatial modulation of the field correlations [26], wherer 苷 r01 uT 具w2典. These modulations are particularlyrelevant for low enough T where r共T兲 # 0, where meanfield theory gives locally ordered regions with characteris-tic size lmø j. We will show that a stripe glass emergesin this temperature regime.An essential prerequisite for the anomalous dynamicalfeatures of glassiness, like aging, memory effects, and836 0031-9007兾00兾85(4)兾836(4)$15.00 © 2000 The American Physical SocietyVOLUME85, NUMBER 4 PHYSICAL REVIEW LETTERS 24JULY2000ergodicity breaking, is most certainly the occurrence ofa large number of metastable states, Nms, separated byenergy barriers which are large compared to the tempera-ture. In viscous liquids undergoing vitrification calorime-try suggests Nms~ exp共constV兲, where V is the systemsize. This observation is the heart of an ideal glass transi-tion scenario based on random first order transitions [27],which was originally motivated by microscopic stabilityanalyses of structural glasses and mean field theories forrandom Potts glasses. Below a crossover temperature,TA,a“viscous,” energy-landscape dominated long timerelaxation sets in due to the occurrence of exponentiallymany metastable states, i.e., the configurational entropy,Sc苷 kBlogNms, becomes extensive. Because of the largebarriers between these states, the system will get stuck forextremely long times in one of the metastable states, i.e.,it will freeze into a glass, at some temperature TG, TAwhich depends, for example, on the cooling rate. Eventhough this laboratory glass transition is purely dynami-cal, a
View Full Document
Unlocking...