On the surface tension of directed linear polymers

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Abstract
The directed polymer model on a two- and three-dimensional lattice in the presence of infinite boundary is solved in the free fermion approximation. The excess surface free energy fs is studied in a wide range of the polymer density p. It is shown that fs ∼ ρ2 for d = 2 and fs ∼ ρ 3/2 for d = 3 when p is small. The law ρ3/2 coincides with that obtained for the surface tension of an isotropic model by scaling arguments

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