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

Infinite-range spin glass3D Coulomb glassequilibriumglass phaseyesequilibriumglass phase?saturatedlinear gapin 1-DOSTABLE I: Critical exponents for the fluid-COP transitionyesalong 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 (contractsFIS-2006-13321-C02-01 and AP2007-01005). The computationswere performed on the Spanish SupercomputingNetwork (RES) node at Universidad de Cantabria.saturatedMP thanks the Aspen Center for Physics where part ofthis work was carried out.scale-freequadratic gapavalanches∗ Electronic address: palassini@ub.edu[1] M. Pollak, Discuss. Faraday Soc. 50, 13 (1970); G. Srinivasan,Phys. Rev. B 4, 2581 (1971).in 1-DOSFIG. 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 the [8] B. Sandow, K. Gloos, R. Rentzsch, A. N. Ionov, and W.(1995).RFIM [12], we expect to be at zero temperature [35]. Assumingthe transition is second order, as we ascertainedSchirmacher, 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. Bby inspecting 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. B70, 214203 (2004).timated β/ν and ¯γ/ν with the quotient method [36] for 52, R3820 (1995).the observables Ms and ¯χ L = N[〈ms 2 〉]av respectively [12] A. Möbius, M. Richter, and B. Drittler, Phys. Rev. B 45,[the quotient estimates from (L, L ′ ) = (6, 8), (6, 10) and 11568 (1992).(8, 10) agree within the errors], while γ/ν was obtained [13] J. H. Davies, P. A. Lee, and T. M. Rice, Phys. Rev. Bby fitting aL γ/ν29, 4260 (1984).to the height of the peak of the susceptibilityN[〈ms 2 〉−〈|ms|〉 2 [14] See e.g. Ref.[21] and references therein.]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,we obtain ν =1.11(12) from the modified hyperscalingrelation [35] (d − θ)ν =2− α, assuming α = 0 and usingθ =¯γ/ν −γ/ν =1.20(20). As shown in Table I, the criticalexponents agree fairly well with the known values formean-fieldB. A. Allgood,and G. Blatter, cond-mat/08054640 (2008).theory[18] A. A. Pastor and V. Dobrosavljević, Phys. Rev. Lett. 83,4642 (1999).[19] S. Pankov and V. Dobrosavljević, Phys. Rev. Lett. 94,046402 (2005).the RFIM [37], which suggests that the system remains [20] M. Müller and L. B. Ioffe, Phys. Rev. Lett. 93, 256403effectively short-range near the transition.(2004).To conclude, our results show that, although meanfieldtheory seems to capture correctly the DOS near the[21] M. Müller and S. Pankov, Phys. Rev. B 75, 144201(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.4beyond mean fieldscale-free?avalanches?Pankov, Dobrosavljevic 2005Müller, Ioffe 2005Müller, Pankov 2007
“Equilibrium glass phase”Infinite-range spin glass3D Coulomb glassTT goverlapP (q)q = 1 N∑Si a Sibparamagnetqi3D mean field theory :(locator approximation)Pankov, Dobrosavljevic 2005Müller, Ioffe 2005Müller, Pankov 2007T < T g ∼ 1/ √ WCHARGE ORDERP (q)Almeida-Thouless lineglassqGoethe, Palassini 2009∼ e αN- Many (# ) equilibrium states- “Marginal criticality”:power law correlations belowT g(〈S i S j 〉−〈S i 〉〈S j 〉) 2 ∼ 1/r θ ijhT0.150.10.050ACFluidBEChargeOrderD0 0.1 0.2 0.3 0.4 0.5WEquilibrium MC:no glass phasedown to verylow T(see alsoSurer et al. 2009)
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 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 and 26: Zero temperature 1-DOSL = 100L = 10
Page 27: conclusionsyessaturatedquadratic ga

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