A self-consistent, conserving mean-field theory for one-particle properties of disordered electronic systems is presented. It is based on a systematic perturbation expansion in 1/Z, where Z is the coordination number of the lattice. To obtain a nontrivial limit for large Z, it is crucial to rescale the hopping integral t according to t -1/&Z. In the limit Z~00, the well-known coherent-potential approximation (CPA) is found to become exact for any lattice. Explicit proofs are presented within the locator and propagator formalism. This explains why CPA often yields quantitatively correct results even for values

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AbslracL Spinless fermions with local disarder and nearest neighbour repulsion are investigaled on a Bethe laltice with infinite branching. 'WO phases are studied: a homogeneous phase and a checkerboard charge-density wave. Within this framework [he model is exaaly solved for all values of disorder, interaction and temperature.' The transition between the RHO phases is described in detail. The density of states p ( w ) , aitical interaction U, and order parameter b are calculakd. Ihe syslem displays anomalous behaviour: away from half-filling particledensity Ruduations due to weak disorder and/or IOW temperatures bvour spontaneous symmetry breaking. W analyse and explain this Unconvenlional phenomenon.

An analytic expression f o r k dynamical conductivity b(m) of spinless fermions with local disorder and nearest-neighbour repulsion is derived on lattices with infinite coordination number 2. The model in exocIly solvable in the whole paramew range assuming two possible phases: a homogeneous phase and a check&Qard chargedensity wave (COW). Away hom half filling the system displays anomalous behaviour: weak particledensity Ruclualions favour spontane~~s symmetry breaking. F m we invesligate UR effects of this anomaly on the wnductivity in Ihe AC and DC regimes. Second. we focus on the Moll transition occurring al rem temperature aI half filling. The critical exponents for the conductivity are computed for the dependence on the interaction U. the disorder y . the filling n. the temperabn'e 7 and the frequency m.

The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in in nite dimensions (d ! 1). In spite of its simplicity the model displays a rich phase diagram depending on the doping , the interaction U and the temperature T . The system can be in the homogeneous phase (hom), the nonsegregated AB charge density wave (ab-cdw), the AB phase separation region (ps-ab/hom; coexistence of ab-cdw and hom), the incommensurate phase (ip) or the IP phase separation region (ps-ab/ip; coexistence of ab-cdw and ip). We identify three important values of the interaction U IPL = 0:572 < U IPH = 1:914 < U IP=PS = 4:212 which distinguish four intervals of U . These imply four di erent types of phase diagrams. In all the three phase diagrams with U below U IP=PS the ip appears. We propose a new general ansatz for the order parameter of this phase. A competition between the ip, the ps-ab/ip and the ps-ab/hom is found. The relevance of our ndings for the phase scenario of the Hubbard model is shown.