Charged Polymers in the Attractive Regime: A First-Order Transition from Brownian Scaling to Four-Point Localization

We study a quenched charged-polymer model, introduced by Garel and Orland in 1988 (Europhys. Lett. 6(7):597–601, 1988; Europhys. Lett. 6(4):307–310, 1988), that reproduces the folding/unfolding transition of biopolymers. We prove that, below the critical inverse temperature, the polymer is delocalized in the sense that: (1) the rescaled trajectory of the polymer converges to the Brownian path; and (2) the partition function remains bounded.