Elastic manifolds in disordered environments: energy statistics

TL;DR

This paper investigates the energy distribution of elastic manifolds in disordered environments at zero temperature, revealing size-dependent probability distributions that transition between Gumbel and non-Gaussian forms based on fluctuation scales.

Contribution

It provides numerical evidence for how energy distributions depend on system size and fluctuation scales, highlighting a crossover to extreme value statistics.

Findings

Energy distribution depends on system size and fluctuation extent.

A crossover to Gumbel distribution occurs when fluctuations are small.

Non-Gaussian, stretched exponential tails appear when fluctuations are comparable.

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 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 cross-over 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.