Elementary excitations and avalanches in the Coulomb ... - PhysioNet

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$J. Phys. A: Math. Gen., Vol. 9. No. 9,1976. Printed in Great Britain ...$

Zero temperature 1-DOSFinite-size effectsSystematic error: repeated runsfor the same sampleW = 2α = 0.499W = 2L = 60" = 0.49910 0 10 -2 10 -1g L (ε) / ε 210 -1L= 163060100PTMC L= 10Shifting range / 23/πg L (!) / ! 2" = 0.510 0 Min of 20 quenchesMax of 20 quenchesOne quench many samples3/#10 -1ε!Shift to reduce chemical potential fluctuations:g(ε) → g(ε − (ε a + ε b )/2)∫ εa−∞dε g(ε) =∫ ∞ε bdε g(ε) =α
conclusionsyessaturatedquadratic gapin 1-DOSyesequilibriumglass phaseno!noyes!2D & 3Dscale-freeavalanchesTABLE I: Critical exponents for the fluid-COP transitionalong BC in Fig. 1, compared with the RFIM values [37].γ/ν ¯γ/ν β/ν νCoulomb glass 1.69(17) 2.89(15) 0.06(3) 1.11(12)RFIM 1.44(12) 2.93(11) 0.011(3) 1.37(9)We thank A.Möbius for helpful correspondence. Thisresearch is supported by the Generalitat de Catalunyaand the Ministerio de Ciencia e Innovación (contractsmean-field theory beyond mean FIS-2006-13321-C02-01 fieldand AP2007-01005). The computationswere performed on the Spanish SupercomputingNetwork (RES) node at Universidad de Cantabria.MP thanks the Aspen Center for Physics where part ofthis work was carried out.Long jumps explain scale free avalanches∗ Electronic address: palassini@ub.edu[1] M. Pollak, Discuss. Faraday Soc. 50, 13 (1970); G. Srinivasan,Phys. Rev. B 4, 2581 (1971).FIG. 4: (Color online) Charge-order correlation length along [2] A. L. Efros and B. I. Shklovskii, J. Phys. C 8, 49 (1975).path BC in Fig. 1. Top inset: order parameter Ms along paths [3] E. I. Levin, V. L. Nguyen, B. I. Shklovskii, and A.AB, BC, and DE. Bottom inset: specific heat along path BC. L. Efros, Sov. Phys. JETP 65, 842 (1987).[4] A. Hunt, Philos. Mag. Lett. 62, 371 (1990).[5] T. Vojta, W. John, and M. Schreiber, J. Phys. Condens.GP does not exist above the dashed line in Fig. 1.Matter 5, 4989 (1993).Critical behavior – Since at W = 0 the fluid-COP transitionhas a positive specific-heat exponent [23], disorder [7] J. G. Massey and M. Lee, Phys. Rev. Lett. 75, 4266[6] See e.g. Ref.[7] and references therein.is relevant [34] and the W ≠ 0 transition will be governedby a random fixed point which, by analogy with theRFIM [12], we expect to be at zero temperature [35]. Assumingthe transition is second order, as we ascertainedBranching process model by inspecting reproduces(1995).the distribution of ms for individual samples,we obtain the critical exponents in Table I. We es-[11] M. Sarvestani, M. Schreiber, and T. Vojta, Phys. Rev. Bwell[8] B. Sandow, K. Gloos, R. Rentzsch, A. N. Ionov, and W.Schirmacher, Phys. Rev. Lett. 86, 1845 (2001).[9] Q. Li and P. Phillips, Phys. Rev. B 49, 10269 (1994).[10] M.H. Overlin, L.A. Wong, and C. C. Yu, Phys. Rev. B70, 214203 (2004).timated β/ν and ¯γ/ν with the quotient method [36] forthe observables Ms and ¯χ L = N[〈ms 2 〉]av respectively[the quotient estimates from (L, L ′ ) = (6, 8), (6, 10) and(8, 10) agree within the errors], while γ/ν was obtainedby fitting aL γ/ν to the height of the peak of the susceptibilityN[〈ms 2 〉−〈|ms|〉 2 [14] See e.g. Ref.[21] and references therein.the avalanche size distributions52, R3820 (1995).[12] A. Möbius, M. Richter, and B. Drittler, Phys. Rev. B 45,11568 (1992).[13] J. H. Davies, P. A. Lee, and T. M. Rice, Phys. Rev. B29, 4260 (1984).]av (data not shown). Thespecific heat cL =1/(NT 2 )[〈H 2 〉 − 〈H〉 2 [15] A. Díaz-Sánchez, M. Ortuño, A. Pérez-Garrido, and]av shows a peak E. Cuevas, Phys. Stat. Sol. (b) 218, 11 (2000).that increases slowly with L (Fig. 4, bottom inset), which [16] E. R. Grannan and C. C. Yu, Phys. Rev. Lett. 71, 3335suggests either α < 0 or a logarithmic divergence (α = 0). (1993).We could not estimate ν directly in a reliable way, but [17] B. Surer, H. G. Katzgraber, G. T. Zimanyi, B. A. Allgood,and G. Blatter, cond-mat/08054640 (2008).we obtain ν =1.11(12) from the modified hyperscaling[18] A. A. Pastor and V. Dobrosavljević, Phys. Rev. Lett. 83,relation [35] (d − θ)ν =2− α, assuming α = 0 and using4642 (1999).θ =¯γ/ν −γ/ν =1.20(20). As shown in Table I, the criticalexponents agree fairly well with the known values forthe RFIM [37], which suggests that the system remainseffectively short-range near the transition.To conclude, our results show that, although meanfieldtheory seems to capture correctly theshape[19] S. Pankov and V. Dobrosavljević, Phys. Rev. Lett. 94,Avalanches have an elongated046402 (2005).[20] M. Müller and L. B. Ioffe, Phys. Rev. Lett. 93, 256403(2004).[21] M. Müller and S. Pankov, Phys. Rev. B 75, 144201DOS near (2007).[22] R. Dickman and G. Stell, cond-mat/9906364 (1999).Coulomb gap, the interaction remains well screened and[23] A. Möbius and U. K. Rößler, cond-mat/0309001 (1999).the correlations remain short-range down to rather low [24] V. Malik and D. Kumar, Phys. Rev. B 76, 125207 (2007).temperatures. If an equilibrium glass phase exists, its [25] A. Möbius, talk given at TIDS11 (2005).onset must be at exceptionally low temperatures.[26] M. Goethe and M. Palassini, in preparation.4open questionsPhysical dynamics: length-dependenthopping rates -> time introduces acutoff in the avalanche size.Avalanches at finite temperatureRelevance for screeningCan avalanches be measured inexperiments?SCE works only qualitatively
Page 1 and 2: Elementary excitations andavalanche
Page 3 and 4: Classical electron glass model (Efr
Page 5 and 6: One-particle energy:ɛɛ i = ∑ j
Page 7 and 8: Dipole excitations:ω ij = ɛ j −
Page 9: Charge avalanches1. Find a local mi
Page 12 and 13: Infinite-range spin glass3D Coulomb
Page 14 and 15: Avalanches and nonlinear screeningB
Page 16 and 17: Avalanche size distribution for dip
Page 18 and 19: # of unstable long hops created (3D
Page 20: Infinite-range spin glass3D Coulomb
Page 23 and 24: Equilibrium finite temperature 1-DO
Page 25: Zero temperature 1-DOSL = 100L = 10

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