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

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 $\varphi =1/(2-\alpha )\simeq 0.5$.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 $\lambda \to 1$.

12 pages, 13 figures

References in corpus (7)

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• Denaturation of Heterogeneous DNA
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• Roles of stiffness and excluded volume in DNA denaturation
• A Simple Model for the DNA Denaturation Transition
• Rare-event induced binding transition of heteropolymers
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Cited by in corpus (7)

• Loop Dynamics in DNA Denaturation
• Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents
• The depinning transition in presence of disorder: a toy model
• Random walks and polymers in the presence of quenched disorder
• Numerical evidence for relevance of disorder in a Poland-Scheraga DNA denaturation model with self-avoidance: Scaling behavior of average quantities
• Delocalization transition of the selective interface model: distribution of pseudo-critical temperatures
• On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder