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

F. Toninelli

Published 2008-06-02, updated 2009-02-25Version 2

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