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We have studied the AC response of a hopping model in the variable range hopping regime by dynamical Monte Carlo simulations. We find that the conductivity as function of frequency follows a universal scaling law. We also compare the numerical results to various theoretical predictions. Finally, we study the form of the conducting network as function of frequency.
We predict the universal power law dependence of localization length on magnetic field in the strongly localized regime. This effect is due to the orbital quantum interference. Physically, this dependence shows up in an anomalously large negative mag
Despite the fact that the problem of interference mechanism of magnetoresistance in semiconductors with hopping conductivity was widely discussed, most of existing studies were focused on the model of spinless electrons. This model can be justified o
We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions or long-range hopping. Based on perturbative arguments there is a common belief
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo simulations st
We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and loca