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

TL;DR

This paper proves that in a random copolymer model at a selective interface, the critical slope in the weak-disorder limit is less than 1, using coarse-graining and fractional moments techniques.

Contribution

It introduces a novel combination of coarse-graining and fractional moments to analyze the critical behavior of random copolymers.

Findings

Critical slope in weak-disorder limit is less than 1

Uses coarse-graining to analyze phase transition

Establishes bounds on fractional moments of the partition function

Abstract

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.