REPLICA SYMMETRY-BREAKING IN ZERO DIMENSION

A simple zero-dimensional model of a disordered system is studied by means of a variational principle for the replicated partition function. The replica symmetric ansatz for the solution of the variational equations gives correct results down to zero temperature if the hamiltonian possesses typically one minimum only. In the complementary case of many metastable states this ansatz as well as a perturbative treatment fail at low temperature. Breaking the symmetry between the replicas in a way known from the mean-field theory of spin glasses one arrives at a consistent description of the low-temperature phase also in the presence of many local minima of the hamiltonian. The results compare well with a scaling analysis and numerical simulations. Because of its simplicity the model may also serve as a pedagogical introduction into the use and the meaning of replica symmetry breaking.