A simple zero-dimensional model of a disordered system is studied by m
eans of a variational principle for the replicated partition function.
The replica symmetric ansatz for the solution of the variational equa
tions gives correct results down to zero temperature if the hamiltonia
n possesses typically one minimum only. In the complementary case of m
any 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 pre
sence of many local minima of the hamiltonian. The results compare wel
l with a scaling analysis and numerical simulations. Because of its si
mplicity the model may also serve as a pedagogical introduction into t
he use and the meaning of replica symmetry breaking.