Thermal Equilibrium with the Wiener Potential: Testing the Replica Variational Approximation
Abstract
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation functions of the Gibbs states may be calculated exactly as a function of the box length and temperature. This allows for a detailed test of results obtained by the replica variational approximation scheme. We show that this scheme provides a reasonable estimate of the averaged free energy. Furthermore our results shed more light on the validity of the concept of approximate ultrametricity which is a central assumption of the replica variational method.
Cite
@article{arxiv.cond-mat/9507099,
title = {Thermal Equilibrium with the Wiener Potential: Testing the Replica Variational Approximation},
author = {Kurt Broderix and Reiner Kree},
journal= {arXiv preprint arXiv:cond-mat/9507099},
year = {2009}
}
Comments
6 pages, 1 file LaTeX2e generating 2 eps-files for 2 figures automatically