Spherical random-field systems with long-range interactions: general results and application to the Coulomb glass

A classical spherical random-field Hamiltonian with long-range (power-law) interactions is investigated by means of the replica theory. Both ferromagnetic and anti-ferromagnetic interactions are considered. The use of continuous variables instead of Ising variables in the spherical version of the model allows one to calculate the free energy exactly. The existence of an equilibrium phase transition is investigated based on the replica-symmetric solution. The results are applied to the Coulomb-glass model of interacting localized electrons in a disordered solid. This model is shown not to have an equilibrium phase transition for spatial dimensions D<or=4. For D>4 the model has a phase transition to an ordered phase; however, it does not have a phase transition to a 'glassy' phase.