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 nonperturbational 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) proportional to L ln L, DeltaE(R) proportional to 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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