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\Ve discuss the bond percolation problem in an anisotropic square lattice using the position space renormalization group. We show that, due to symmetry, this treatment reproduces known exact results for this problem. The phase cliagram and the Bow lines m parameter space are also shown. Our results are in agreement with universality.

Theoretical aspects of the MSXα method are analyzed. It is shown that real field self-consistency is not achieved in an MSXα calculation and some consequences of this fact are discussed. The approximations involved in the use of the transition-state procedure to evaluate ionization and excitation energies from a MSXα calculation are presented in some detail and commented.

The SCF-MSXα method is applied in the study of the electronic structure of F centers in CaF2, SrF2, and BaF2. The predicted optical transition energies are in disagreement with the experimental data. An explanation for the discrepancy is provided showing the inadequacy of the spherical averaging of the potential within the muffin-tin approximation. La methode SCF-MSXα a ete utilisee pour la determination de la structure electronique des centres F dans CaF2, SrF2 et BaF2. Les energies calculees pour les transitions optiques sont en desaccord avec les resultats experimentaux. Une interpretation de ce desaccord a ete fournie montrant que la moyenne spherique du potentiel dans l'approximation “muffin-tin” n'est pas adequate en ce cas.

The authors present a calculation of the bond percolation problem in a square lattice in presence of a 'magnetic field', using the position space renormalisation group and cells of dimension b*b, where b runs from 2 up to 5. Due to symmetry, the calculation splits into two parts, one determining the 'thermal' exponent nu and the other, the 'magnetic' exponent eta . For the largest cell in each case, one gets nu =1.355 (b=5) and eta =0.244 (b=4), in good agreement with series results of Dunn et al. (1975). Comments are made on the extrapolation of the results to b= infinity .

a square lattice with firstand second-neighbor bonds. We treat the respective prob abilities as independent variables. Two types of cells are constructed. In one of them we consider the lattice as two interpenetrating sublattices, first-neighbor bonds playing the role of intersublattice links. This allows the calculation of both critical exponents v and y, without resorting to nivailable in the literature. The phase diagram in parameter space is also obtained in e lch cise.

A two-parameter real-space renormalization-group approach to the site-percolation problem in a square lattice is proposed. The two parameters are the concentration $p$ of active first-neighbor bonds, and the concentration $q$ of occupied sites. From these two parameters one can calculate two independent critical exponents, and the others can be obtained through scaling relations, with no need of external applied fields.