Universal energy distribution for interfaces in a random field environment

TL;DR

This paper investigates the energy distribution of interfaces in a random field environment at zero temperature, revealing a universal Gumbel distribution for large systems and analyzing the effects of disorder through perturbation and renormalization techniques.

Contribution

It introduces a comprehensive analysis combining perturbation expansion and functional renormalization group to characterize the energy distribution in disordered interfaces.

Findings

Average energy scales as L log L

Energy variance scales as L

Distribution converges to Gumbel distribution for large L

Abstract

We study the energy distribution function $\rho (E)$ for interfaces in a random field environment at zero temperature by summing the leading terms in the perturbation expansion of $\rho (E)$ in powers of the disorder strength, and by taking into account the non perturbational effects of the disorder using the functional renormalization group. We have found that the average and the variance of the energy for one-dimensional interface of length $L$ behave as, $<E>_{R}\propto L\ln L$, $\Delta E_{R}\propto L$, while the distribution function of the energy tends for large $L$ to the Gumbel distribution of the extreme value statistics.