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Monte Carlo simulations for the site percolation problem are presented for lattices up to 64 x 10 6 sites. We investigate for the square lattice the variable-range percolation problem, where distinct trends with bond-length are found for the critical concentrations and for the critical exponents?? and?? . We also investigate the layer problem for stacks of square lattices added to approach a simple cubic lattice, yielding critical concentrations as a functional of layer number as well as the correlation length exponent?? . We also show that the exciton migration probability for a common type of ternary lattice system can be described by a cluster model and actually provides a cluster generating function.

In this paper a group theoretical approach was employed for the classification and construction of molecular exciton wavefunctions for two important crystal structures (naphthalene--anthracene and benzene), utilizing the representation theory of finite groups. The generally valid scheme requires only cyclic boundary conditions (being explicitly imposed on all space group operations, including rotations and reflections). Even though these symmetry considerations are insufficient to determine crystal wavefunctions belonging to a general k vector, it is still possible to write a simple expression for such wavefunctions. This is achieved for cases where the nonvanishing exciton transfer integrals are confined to molecular interactions along symmetry axes and/or planes.