2005/02/08 by Thomas Garel, T. Garel, Cecile Monthus +1 · 1 citation
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.soft #math.PR
paper · pdf · doi:10.1140/epjb/e2005-00241-1
published as Eur. Phys. J. B 46, 117 (2005) · 12 pages, 13 figures
arxiv created 2005/02/08 · openalex publication_date 2005/07/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 ∼ 105 to 106, with 104 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) ≃ 0.5.We then analyse at criticality the distribution of loop length l in both regimes l ∼ O(N) and 1 ≪ l ≪ 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→ 1.