THERMAL-EQUILIBRIUM WITH THE WIENER POTENTIAL - TESTING THE REPLICA VARIATIONAL APPROXIMATION

We consider the statistical mechanics of a classical particle in a one -dimensional box subjected to a random potential which constitutes a W iener process on the coordinate axis. The distribution of the free ene rgy and all correlation functions of the Gibbs states may be calculate d exactly as a function of the box length and temperature. This allows for a detailed test of results obtained by the replica-variational-ap proximation scheme. We show that this scheme provides a reasonable est imate of the averaged free energy. Furthermore our results shed more l ight on the validity of the concept of approximate ultrametricity whic h is a central assumption of the replica variational method.