Some Statistical Properties Of Disordered Systems With Coulomb Interaction

The combined influence of disorder and long-range interaction on the properties of many particles system has been a subject of great interest for a long time. The competition between Coulomb repulsion and disorder produces a Coulomb glass which is an amorphous insulator. A great deal of effort has been expanded in studying various thermodynamic properties of the Coulomb glass such as the specific heat, the presence of a Coulomb glass phase transition in which the electrons are frozen into a highly disordered arrangement, the electrical conductivity and the Coulomb gap and so forth.On the other hand, Fractals are ubiquitous in nature and the study of their physical properties has considerably universal significance. During the past two decades, there has been much attention devoted to fractal systems. It has now been well-known that in fractal framework noninteracting electron systems exhibit many unusual features including fractal energy spectra and fractal wave functions. Therefore, studies on these systems in the presence of interaction should also be a quite interesting problem physically. Motivated by the idea, we firstly focus on zero-temperature static properties of the Coulomb glass in the framework of fractal. On the theoretical side, we propose by means of a qualitatively analytical consideration that the behavior of the single-electron density of states close to the Fermi energy scales as ρ(ε) ^|ε-μ|^D_f-1 for fractal dimension D_f . Subsequently, we carry out a series of Monte Carlo simulations for different disorder distributions over a wide range of disorder strengths. The numerical results demonstrate that the Coulomb repulsion between the localized electrons does cause a universal gap in the single-electron density of states near the Fermi energy whose form is in reasonable agreement with our scaling predictions. In addition, we find that the asymptotic scaling behavior is independent of distributions and strengths of disorder.Another focus of this paper is to determine some general thermodynamics of the Coulomb glass constrained to a two-dimensional square lattice, for the first time ever, from the multi-canonical Monte Carlo simulations. Our data are well consistent with earlier simulations mainly by means of the conventional Metropolis algorithm. Numerical results clearly show that the Coulomb gap in the single-electron density of states is filled gradually up as the temperature increases. The averaged occupancies over sites conform to the Fermi function to perfection as derived theoretically. Considering that the energy landscape of the glassy system is characterized by a multitude of local minima separated by high-energy barriers, we wish to point out that the multicanonical Monte Carlo method should be remarkably superior to the Metropolis algorithm in speeding up such systems. This once more confirms the advantage of the multicanonical sampling techniques which has been successfully applied to many complex situations such as...