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We reply to the Comment by Mobius and Richter [arXiv:0908.3092, Phys. Rev. Lett. 105, 039701 (2010)] on Density of States and Critical Behavior of the Coulomb Glass [arXiv:0805.4640, Phys. Rev. Lett. 102, 067205 (2009)] and address the issues raised with our results on the density of states. In addition, we correct our statements about the random displacement version of the Coulomb glass model where the Wigner crystal is not as robust to disorder as stated. Still, our main result of a lack of a finite-temperature transition in the Coulomb glass remains unchallenged.
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We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L=40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain Tc = 1.1019(29) for the critical temperature, u = 2.562(42) for the thermal exponent, eta = -0.3900(36) for the anomalous dimension and omega = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield alpha = -5.69(13), beta = 0.782(10) and gamma = 6.13(11). We also compute several universal quantities at Tc.
In Phys. Rev. Lett. 110, 219701 (2013) [arXiv:1211.0843] Billoire et al. criticize the conclusions of our Letter [Phys. Rev. Lett. 109, 177204 (2012), arxiv:1206.0783]. They argue that considering the Edwards-Anderson and Sherrington-Kirkpatrick models at the same temperature is inappropriate and propose an interpretation based on the replica symmetry breaking theory. Here we show that the theory presented in the Comment does not explain our data on the Edwards-Anderson spin glass and we stand by our assertion that the low-temperature behavior of the Edwards-Anderson spin glass model does not appear to be mean-field like.
The existence of an equilibrium glassy phase for charges in a disordered potential with long-range electrostatic interactions has remained controversial for many years. Here we conduct an extensive numerical study of the disorder-temperature phase diagram of the three-dimensional Coulomb glass model using population annealing Monte Carlo to thermalize the system down to extremely low temperatures. Our results strongly suggest that, in addition to a charge order phase, a transition to a glassy phase can be observed, consistent with previous analytical and experimental studies.
We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure states regarding a controversial statistic, characterizing the fraction of centrally peaked disorder instances, of the overlap function order parameter. We observe that this statistic is subtly and sensitively influenced by the slight fluctuations of the integrated central weight of the disorder-averaged overlap function, making the asymptotic growth behaviour very difficult to identify. Modified statistics effectively reducing this correlation are studied and essentially monotonic growth trends are obtained. The effect of temperature is also studied, finding a larger growth rate at a higher temperature. Our state-of-the-art simulation and variance reduction data analysis suggest that the many pure state picture is most likely and coherent.
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.
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