The finite connectivity spin glass: investigation of replica symmetry breaking of the ground state

The free energy of the fixed finite connectivity spin glass is investigated in detail and the authors prove the equivalence of different forms which were obtained in the literature using completely different methods. Furthermore, the question of replica symmetry breaking is examined for low connectivity. They find by a variational calculation that even for a first-step breaking one can obtain a more optimal value for the ground state energy by going beyond the simple ansatz of Wong-Sherrington (1988) of totally uncorrelated groups of replicas.