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For a much-studied model of random copolymer at a selective interface weprove that the slope of the critical curve in the weak-disorder limit isstrictly smaller than 1, which is the value given by the annealed inequality.The proof is based on a coarse-graining procedure, combined with upper boundson the fractional moments of the partition function.

Coarse graining, fractional moments and the critical slope of random copolymers