04-201 T. Bodineau, G. Giacomin

On the localization transition of random copolymers near selective interfaces. (266K, PDF) Jun 28, 04

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Abstract. In this note we consider the (de)localization transition for random directed $(1+1)$--dimensional copolymers in the proximity of an interface separating selective solvents. We derive a rigorous lower bound on the free energy that yields a substantial improvement on the bounds from below on the critical line that were known so far. This implies a lower bound on the critical curve which coincides with the critical curve conjectured by C. Monthus on the base of a renormalization group analysis. We discuss this result in the light of the (rigorous and non rigorous) approaches present in the literature and, by making an analogy with a particular asymptotics of a disordered wetting model, we propose a simplified framework in which the question of identifying the critical curve, as well as understanding the nature of the transition, may be approached.

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