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

Simple item page
dc.creatorGarel, Thomas
dc.creatorMonthus, Cecile
dc.date2005-02-08
dc.date.accessioned2026-07-07T03:03:38Z
dc.date.available2026-07-07T03:03:38Z
dc.descriptionWe 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 $ϕ=1/(2-α) \simeq 0.5$.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 $λ=l/N$ as $λ\to 1$.
dc.description12 pages, 13 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0502195
dc.identifierhttp://arxiv.org/abs/cond-mat/0502195
dc.identifierEur. Phys. J. B 46, 117 (2005)
dc.identifierdoi:10.1140/epjb/e2005-00241-1
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/25827
dc.subjectDisordered Systems and Neural Networks
dc.subjectSoft Condensed Matter
dc.subjectProbability
dc.titleTwo-dimensional wetting with binary disorder: a numerical study of the loop statistics
dc.typetext

Files

Collections

arXiv