Universal energy distribution for interfaces in a random field environment

Details Universal energy distribution for interfaces in a random field environment Universal energy distribution for interfaces in a random field environment

2003-02-21

arxiv.org/abs/cond-mat/0302444v2

Phys. Rev. E 68, 056115 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 2 figures, revtex4; the distribution function of the total and the disorder energy is included

Scientific paper

10.1103/PhysRevE.68.056115

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, $_{R}\propto L\ln L$, $\Delta E_{R}\propto L$, while the distribution function of the energy tends for large $L$ to the Gumbel distribution of the extreme value statistics.

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