Random polymers and delocalization transitions

TL;DR

This paper reviews phase transition properties in disordered systems, emphasizing correlation behaviors, critical exponents, and non-self-averaging, and discusses recent findings on delocalization transitions in various random polymer models.

Contribution

It provides a comprehensive summary of general properties of phase transitions with quenched disorder and presents recent results on delocalization transitions in multiple random polymer models.

Findings

Distinct correlation length exponents can exist in disordered systems.

Thermodynamic observables lack self-averaging at criticality.

Distribution of pseudo-critical temperatures scales with system size.

Abstract

In these proceedings, we first summarize some general properties of phase transitions in the presence of quenched disorder, with emphasis on the following points: the need to distinguish typical and averaged correlations, the possible existence of two correlation length exponents $\nu$, the general bound $\nu_{FS} \geq 2/d$, the lack of self-averaging of thermodynamic observables at criticality, the scaling properties of the distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples of size $L$. We then review our recent works on the critical properties of various delocalization transitions involving random polymers, namely (i) the bidimensional wetting (ii) the Poland-Scheraga model of DNA denaturation (iii) the depinning transition of the selective interface model (iv) the freezing transition of the directed polymer in a random medium.