Lower bounds for the ground-state degeneracies of frustrated systems on fractal lattices

The total number of ground states for nearest-neighbor-interaction Ising sy stems with frustrations, defined on hierarchical lattices, is investigated. A simple method is presented, which allows one to factorize the ground-sta te degeneracy, at a given hierarchy level n, in terms of contributions due to all hierarchy levels. Such a method may yield the exact ground-state deg eneracy of uniformly frustrated systems, whereas it works as an approximati on for randomly frustrated models. In the latter cases, it is demonstrated that such an approximation yields lower-bound estimates for the ground-stat e degeneracies.