Abstract
The wetting transition in the presence of a random substrate is studied in two dimensions, using a restricted solid-on-solid model. The singular part of the quenched free energy and specific heat is calculated exactly by means of the replica trick. Disorder introduces logarithmic corrections to the results of the pure system. The divergent part of the width of the wetting layer is also evaluated: here no corrections to the pure case are obtained. The method employed uses a field-theoretic calculation (in terms of Goldstone diagrams) of the ground-state energy of an effective many-body Hamiltonian. The validity of the replica method is tested numerically.
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Forgacs, G., Luck, J.M., Nieuwenhuizen, T.M. et al. Exact critical behavior of two-dimensional wetting problems with quenched disorder. J Stat Phys 51, 29–56 (1988). https://doi.org/10.1007/BF01015319
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DOI: https://doi.org/10.1007/BF01015319