title: Lower bounds for the ground-state degeneracies of frustrated systems on fractal lattices
abstract: The total number of ground states for nearest-neighbor-interaction Ising systems with frustrations, defined on hierarchical lattices, is investigated. A simple method is presented, which allows one to factorize the ground-state 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 degeneracy of uniformly frustrated systems, whereas it works as an approximation for randomly frustrated models. In the latter cases, it is demonstrated that such an approximation yields lower-bound estimates for the ground-state degeneracies.
authors.affiliation: Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil.
authors.initials: EM
authors.lastname: Curado
authors.initials: FD
authors.lastname: Nobre