Elastic manifolds in disordered environments: Energy statistics

¹ Helsinki University of Technology, Laboratory of Physics P.O. Box 1100, FIN-02015 HUT, Finland
² Lawrence Livermore National Laboratory - 7000 East Avenue, L-415 Livermore, CA 94550, USA

Received: 12 December 2002
Accepted: 30 January 2003

Abstract

The energy of an elastic manifold in a random landscape at T=0 is shown numerically to obey a probability distribution that depends on the size of the box it is put into. If the extent of the spatial fluctuations of the manifold is much less than that of the system, a crossover takes place to the Gumbel distribution of extreme statistics. If they are comparable, the distributions have non-Gaussian, stretched exponential tails. The low-energy and high-energy stretching exponents are roughly independent of the internal dimension and the fluctuation degrees of freedom.