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 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 $g(ϵ,T)=T^{\delta }f(|ϵ|/T)$ with $\delta =2.01\pm 0.05$ 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 charge-ordered phase.

We study numerically the statistics of elementary excitations and charge avalanches in the classical Coulomb glass model of localized charges with unscreened Coulomb interaction and disorder. We compute the single-particle density of states with an energy minimization algorithm for systems of up to 100³ sites. The shape of the Coulomb gap is consistent with a power-law with exponent δ 2.4 and marginally consistent with exponential behavior. The results are also compared with a recently proposed self-consistent approach. We then analyze the size distribution of the charge avalanches produced by a small perturbation of the system. We show that the distribution decays as a power law in the limit of large system size, and explain this behavior in terms of the elementary excitations. Similarities and differences with the scale-free avalanches observed in mean-field spin glasses are discussed.

The mutual information expansion (MIE) represents an approximation of the configurational entropy in terms of low-dimensional integrals. It is frequently employed to compute entropies from simulation data of large systems, such as macromolecules, for which brute-force evaluation of the full configurational integral is intractable. Here, we test the validity of MIE for systems consisting of more than m = 100 degrees of freedom (dofs). The dofs are distributed according to multivariate Gaussian distributions which were generated from protein structures using a variant of the anisotropic network model. For the Gaussian distributions, we have semi-analytical access to the configurational entropy as well as to all contributions of MIE. This allows us to accurately assess the validity of MIE for different situations. We find that MIE diverges for systems containing long-range correlations which means that the error of consecutive MIE approximations grows with the truncation order n for all tractable n $\ll$ m. This fact implies severe limitations on the applicability of MIE, which are discussed in the article. For systems with correlations that decay exponentially with distance, MIE represents an asymptotic expansion of entropy, where the first successive MIE approximations approach the exact entropy, while MIE also diverges for larger orders. In this case, MIE serves as a useful entropy expansion when truncated up to a specific truncation order which depends on the correlation length of the system.