The Critical Curve of the Random Pinning and Copolymer Models at Weak Coupling

Abstract

We study random pinning and copolymer models, when the return distribution of the underlying renewal process has a polynomial tail with finite mean. We compute the asymptotic behavior of the critical curves of the models in the weak coupling regime, showing that it is universal. This proves a conjecture of Bolthausen, den Hollander and Opoku for copolymer models (ref. [8]), which we also extend to pinning models.

Added a heuristic explanation, updated references, and other minor changes; version to appear on CMP

References in corpus (7)

• Fractional moment bounds and disorder relevance for pinning models
• Smoothing effect of quenched disorder on polymer depinning transitions
• A replica-coupling approach to disordered pinning models
• A numerical approach to copolymers at selective interfaces
• Copolymers at selective interfaces: new bounds on the phase diagram
• A general smoothing inequality for disordered polymers
• A copolymer near a selective interface: variational characterization of the free energy

Cited by in corpus (7)

• Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift
• Universality for the pinning model in the weak coupling regime
• Scaling limits of disordered systems and disorder relevance
• The random pinning model with correlated disorder given by a renewal set
• Polynomial chaos and scaling limits of disordered systems
• The continuum disordered pinning model
• The critical disordered pinning measure