We investigate the lattice Coulomb glass model in three dimensions via Monte Carlo simulations. No evidence for an equilibrium glass phase is found down to very low temperatures, although the correlation length increases rapidly near T=0. A charge-ordered phase (COP) exists at low disorder. The transition to this phase is consistent with the Random Field Ising universality class, which shows that the interaction is effectively screened at moderate temperature. For large disorder, the single-particle density of states near the Coulomb gap satisfies the scaling relation g(e,T)=T^δf(|e|/T) with δ= 2.01 +/- 0.05 in agreement with the prediction of Efros and Shklovskii. For decreasing disorder, a crossover to a larger effective exponent occurs due to the proximity of the COP.
We show that introducing long-range Coulomb interactions immediately lifts the massive ground state degeneracy induced by geometric frustration for electrons on quarter-filled triangular lattices in the classical limit. Important consequences include the stabilization of a stripe-ordered crystalline (global) ground state, but also the emergence of very many low-lying metastable states with amorphous "stripe-glass" spatial structures. Melting of the stripe order thus leads to a frustrated Coulomb liquid at intermediate temperatures, showing remarkably slow (viscous) dynamics, with very long rel…
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 employ Monte Carlo simulations to study the relaxation properties of the two-dimensional Coulomb glass in disordered semiconductors and the three-dimensional Bose glass in type-II superconductors in the presence of extended linear defects. We investigate the effects of adding non-zero random on-site energies from different distributions on the properties of the correlation-induced Coulomb gap in the density of states (DOS) and on the non-equilibrium aging kinetics highlighted by the density autocorrelation functions. We also probe the sensitivity of the system's equilibrium and non-equilibr…
Reply to Comment "Density of states and critical behavior of the three-dimensional Coulomb Glass"
我们回答莫比乌斯和里希特的评论[arXiv：0908.3092，物理。105，039701（2010）]关于“Density of States and Critical Behavior of the Coulomb Glass”[arXiv：0805.4640，Phys.Rev.Lett. 102，067205（2009）]，并解决我们的结果对状态密度提出的问题。此外，我们纠正我们的声明的随机位移版本的库仑玻璃模型的维格纳晶体是不稳定的无序。尽管如此，我们的主要结果，缺乏一个有限的温度转变的库仑玻璃仍然没有受到挑战。
We have annealed two dimensional lattice model of Coulomb glass using Monte Carlo simulations to obtain the ground state. We have shown that the energy required to create a domain of linear size L in d dimensions is proportional to $L^{d-1}$. Using Imry-Ma arguments given for RFIM, one gets $d_{c}\geq 2$ for Coulomb glass. The investigations in the transition region shows that the domain wall of the metastable state in the charge-ordered phase shifts as disorder is increased to give disordered ground state at higher disorder strength indicating phase coexistence. This coupled with discontinuit…
We have studied the ground states of two dimensional lattice model of Coulomb Glass via Monte Carlo annealing. Our results show a possibility of existence of a critical disorder (Wc) below which the system is in the charge ordered phase and above it the system is in the disordered phase. We have used finite size scaling to calculate Wc = 0.2413, the critical exponent of magnetization β = 0 indicating discontinuity in magnetization and the critical exponent of correlation length ν = 1.0. The distribution of staggered magnetization for different disorder strengths shows a three peak structure. W…
We explore the stability of far-from-equilibrium metastable states of a three-dimensional Coulomb glass at zero temperature by studying charge avalanches triggered by a slowly varying external electric field. Surprisingly, we identify a sharply defined dynamical ("depinning") phase transition from stationary to nonstationary charge displacement at a critical value of the external electric field. Using particle-conserving dynamics, scale-free system-spanning avalanches are observed only at the critical field. We show that the qualitative features of this depinning transition are completely diff…
Comment on "Density of States and Critical Behavior of the Coulomb Glass"
在最近对库仑玻璃的数值研究中，Surer等人[Phys. Rev. Lett. 102，067205（2009）]得出结论，他们的模拟结果与Efros Shklovskii对三维情况下态密度的预测一致。在这里，我们表明，这种说法没有相关的问题的渐近行为的库仑间隙，因为它是基于不合理的假设。此外，对于随机位移库仑玻璃模型，我们证明了一部分的状态密度数据由Sureer等人。错误地表现出一个广泛的差距。这与交错占领不稳定有关，与他们的调查结果相反。
We present numerical evidence using Monte Carlo simulations of finite-temperature phase transition in two dimensional Coulomb Glass lattice model with random site energies at half-filling. For the disorder strengths ($W$) studied in this paper, we find the existence of charge-ordered phase (COP) below the critical temperature ($T_{c}(W)$). Also, the probability distribution of staggered magnetization calculated at each W shows a two-peak structure at their respective critical temperature. Thus the phase transition from fluid to COP as a function of temperature is second order for all $W$. We f…
We study spin glass behavior in a random Ising Coulomb antiferromagnet in two and three dimensions using Monte Carlo simulations. In two dimensions, we find a transition at zero temperature with critical exponents consistent with those of the Edwards Anderson model, though with large uncertainties. In three dimensions, evidence for a finite-temperature transition, as occurs in the Edwards-Anderson model, is rather weak. This may indicate that the sizes are too small to probe the asymptotic critical behavior, or possibly that the universality class is different from that of the Edwards-Anderson…
In this paper, we analyze the dynamics of the Coulomb Glass lattice model in three dimensions near a local equilibrium state by using mean-field approximations. We specifically focus on understanding the role of localization length ($ξ$) and the temperature ($T$) in the regime where the system is not far from equilibrium. We use the eigenvalue distribution of the dynamical matrix to characterize relaxation laws as a function of localization length at low temperatures. The variation of the minimum eigenvalue of the dynamical matrix with temperature and localization length is discussed numerical…
In this paper, we have studied the three dimensional Coulomb glass lattice model at half-filling using Monte Carlo Simulations. Annealing of the system shows a second-order transition from paramagnetic to charge-ordered phase for zero as well as small disorders. We have also calculated the critical exponents and transition temperature using a finite sizing scaling approach. The Monte Carlo simulation is done using the Metropolis algorithm, which allowed us to study larger lattice sizes. The transition temperature and the critical exponents at zero disorder matched the previous studies within n…
A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields $B \ll H_{c2}$ at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase -- such as $\mathrm{In O}_x$, $\mathrm{Nb N}$, $\mathrm{Ti N}$, $\mathrm{Mo Ge}$, nano-granular aluminium, and others -- is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state o…
Taking into account the interplay between the disorder and Coulomb interaction, the phase diagram of three-dimensional anisotropic Weyl semimetal is studied by renormalization group theory. Weak disorder is irrelevant in anisotropic Weyl semimetal, while the disorder becomes relevant and drives a quantum phase transition from semimetal to compressible diffusive metal phases if the disorder strength is larger than a critical value. The long-range Coulomb interaction is irrelevant in clean anisotropic Weyl semimetal. However, interestingly, we find that the long-range Coulomb interaction exerts …
We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at $T\sim 0$. The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using Baranovskii et al algorithm followed by cluster flipping to obtain the pseudo ground states. We have shown that the energy required to create a domain of linear size L in d dimensions is proportional to $L^{d-1}$. Using Imry-Ma arguments given for random field Ising model, one gets critical dimension $d_{c}\geq 2$ for Coulomb glass. The investigations of doma…
The lattice model of Coulomb Glass in two dimensions with box-type random field distribution is studied at zero temperature for system size upto $96^{2}$. To obtain the minimum energy state we annealed the system using Monte Carlo simulation followed by further minimization using cluster-flipping. The values of the critical exponents are determined using the standard finite size scaling. We found that the correlation length $ξ$ diverges with an exponent $ν=1.0$ at the critical disorder $W_{c} = 0.2253$ and that $χ_{dis} \approx ξ^{4-\barη}$ with $\barη=2$ for the disconnected susceptibility. T…
We present a comprehensive investigation of the magnetic properties of stage-1 graphite intercalated FeCl$_3$ using a combination of DC and AC magnetic susceptibility, thermoremanent magnetization and field dependent magnetization measurements. This van der Waals system, with a centrosymmetric honeycomb lattice, combines frustration and disorder, due to intercalation, and may be hosting topologically non-trivial magnetic phases. Our study identifies two magnetic phase transitions at $T_{f1} \approx $ 4.2 K and at $T_{f2} \approx $ 2.7 K. We find that the paramagnetic state, for $T > T_{f1}$, i…
The exact 2-point function of certain physically motivated operators in SYK-like spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all time scales. The main tool developed is a new approach to the combinatorics of chord diagrams, allowing to rewrite the spin glass system using an auxiliary Hilbert space, and Hamiltonian, built on the space of open chord diagrams. We argue the latter can be interpreted as the bulk description and that it reduces to the Schwarzian action in the low energy lim…
Relaxation of the Random Site Coulomb glass Model in Two Dimensions
Faculty of Physical Sciences, South Asian University（南亚大学物理科学学院）；Faculty of Interdisciplinary Studies, South Asian University（南亚大学跨学科研究学院）；Department of Physics and Material Science, Jaypee Institute of Information Technology（贾伊皮信息技术大学物理与材料科学系）
We propose a duality analysis for obtaining the critical manifold of two-dimensional spin glasses. Our method is based on the computation of quenched free energies with periodic and twisted periodic boundary conditions on a finite basis. The precision can be systematically improved by increasing the size of the basis, leading to very fast convergence towards the thermodynamic limit. We apply the method to obtain the phase diagrams of the random-bond Ising model and $q$-state Potts gauge glasses. In the Ising case, the Nishimori point is found at $p_N = 0.10929 \pm 0.00002$, in agreement with a…
