We study the spherical version of a model of localized particles in a random potential which are subject to a power-law interaction Uij ~ rij-σ. In the case of a repulsive interaction with σ = 1 the model is identical to the spherical version of the Coulomb-glass model of disordered localized electrons. The use of continuous variables instead of discrete occupation numbers of the sites renders the model exactly solvable. Analytic results are obtained for the free energy and for the single-particle density of states (DOS) as an example for single-particle properties. The zero-temperature DOS shows a hard gap close to the chemical potential.
T. Vojta and M. Schreiber, "Generalized Coulomb Gap in the Spherical Version of a Lattice Model of Disordered and Correlated Localized Particles," Physical Review B, vol. 49, no. 12, pp. 7861-7867, American Physical Society (APS), Mar 1994.
The definitive version is available at http://dx.doi.org/10.1103/PhysRevB.49.7861
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