MONTE-CARLO SIMULATIONS OF SPATIAL CORRELATIONS OF CHARGES ON A RANDOM LATTICE - POSITIONAL VERSUS THERMAL DISORDER

Monte Carlo simulations of a system of point charges occupying a fract ion of a random array of sites in two and three dimensions are reporte d. We focus on the Coulomb-interaction-driven ordering phenomena in th e system. The model corresponds directly to the details of physics of charges of partially filled resonant impurities in a semiconductor, bu t qualitative results are of wider significance. Spatial correlations of charges, due to long-range repulsive interactions between them, are studied as a function of temperature by means of pair correlation fun ctions and one-particle density of states. The presence of inherent di sorder of the allowed positions of the impurity charges is found to in fluence the ordering process, leading to a saturation of correlation r ange at low temperatures. Such behaviour is not observed in a pseudo-l iquid model also studied for the sake of comparison. Within the latter model the charges are assumed to have the same densities, and interac tions to have the same strength, but instead of being restricted to a random array of sites the charges are allowed to take any position. Co mparison of the two models allows us to introduce a phenomenological e ffective temperature, which includes the effects of the built-in disor der on the same footing as the thermal disorder. The formation of the Coulomb gap in the density of states is discussed and its relation to the Madelung gap in crystalline materials pointed out.