Two-dimensional wetting with binary disorder: a numerical study of the loop statistics

TL;DR

This study numerically investigates the wetting transition of a polymer on a disordered substrate, revealing that critical exponents match the pure case but with significant logarithmic corrections due to disorder.

Contribution

It introduces a numerical approach using the Poland-Scheraga model with Fixman-Freire scheme to analyze loop statistics in disordered wetting transitions.

Findings

Critical exponents are similar to the pure case.

Logarithmic corrections significantly affect thermodynamics.

Disorder induces a logarithmic singularity in loop distribution.

Abstract

We numerically study the wetting (adsorption) transition of a polymer chain on a disordered substrate in 1+1 dimension.Following the Poland-Scheraga model of DNA denaturation, we use a Fixman-Freire scheme for the entropy of loops. This allows us to consider chain lengths of order $N \sim 10^5 $ to $10^6$, with $10^4$ disorder realizations. Our study is based on the statistics of loops between two contacts with the substrate, from which we define Binder-like parameters: their crossings for various sizes $N$ allow a precise determination of the critical temperature, and their finite size properties yields a crossover exponent $\phi=1/(2-\alpha) \simeq 0.5$.We then analyse at criticality the distribution of loop length $l$ in both regimes $l \sim O(N)$ and $1 \ll l \ll N$, as well as the finite-size properties of the contact density and energy. Our conclusion is that the critical exponents for the thermodynamics are the same as those of the pure case, except for strong logarithmic corrections to scaling. The presence of these logarithmic corrections in the thermodynamics is related to a disorder-dependent logarithmic singularity that appears in the critical loop distribution in the rescaled variable $\lambda=l/N$ as $\lambda \to 1$.