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We derive a low-energy Hamiltonian for the elastic energy of a N\'eel domainwall in a thin film with in-plane magnetization, where we consider thecontribution of the long-range dipolar interaction beyond the quadraticapproximation. We show that such a Hamiltonian is analogous to the Hamiltonianof a one-dimensional polaron in an external random potential. We use a replicavariational method to compute the roughening exponent of the domain wall forthe case of two-dimensional dipolar interactions.Comment: REVTEX, 35 pages, 2 figures. The text suffered minor changes and  references 1,2 and 12 were added to conform with the referee's repor

Domain wall roughening in dipolar films in the presence of disorder