The Coulomb gap and low energy statistics for Coulomb glasses
We study the statistics of local energy minima in the configuration space of two-dimensional lattice Coulomb glasses with site disorder and the behavior of the Coulomb gap depending on the strength of random site energies. At intermediate disorder, i.e., when the typical strength of the disorder is of the same order as the nearest-neighbor Coulomb energy, the high energy tail of the distribution of the local minima is exponential. We furthermore analyze the structure of the local minima and show that most sites of the system have the same occupation numbers in all of these states. The density of states (DOS) shows a transition from the crystalline state at zero disorder (with a hard gap) to an intermediate, probably glassy state with a Coulomb gap. We analyze this Coulomb gap in some detail and show that the DOS deviates slightly from the traditional linear behavior in 2D. For finite systems these intermediate Coulomb gap states disappear for large disorder strengths and only a random localized state in which all electrons are in the minima of the random potential exists. Dedication: This paper is dedicated to Thomas Nattermann, our dearest friend, brilliant colleague, and outstanding teacher.
Coulomb gap in two- and three-dimensional systems: Simulation results for large samples.
Computer experiments have been performed to study the single-particle density of states, g(E), in the Coulomb gap. This gap occurs in disordered insulating systems as an effect ofthe long-range tail of the Coulomb interaction. In order to compare these numerical results with the analytical theory on a broader energy scale than previous authors, very large samples have been considered, up to 40000 and 125000 sites for dimensions d=2 and 3, respectively. Special algorithms have been developed for this aim
Two-dimensional Ising model in random magnetic fields
The statistical mechanics of finite L×L Ising square lattices in a field ±h of random sign is investigated numerically by a modified recursive transfer matrix method for 6<~L<~16. Our results are consistent with the absence of a spontaneous magnetization for h≠0 even in the ground state. The singularities occurring at T=0 in the range 0<~h<~4J, J being the exchange constant, are discussed in terms of a cluster expansion. For nonzero T, less than the critical temperature of the pure two-dimensional Ising model, and h sufficiently small, the system exhibits a nonzero spin-glass order parameter of the Mattis type although there is no magnetization. The ferromagnetic correlation function becomes long ranged for h→0 and is calculated from the domain-wall density.