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

摘要

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 similar to 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 de. ne 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) similar or equal to 0.5. We then analyse at criticality the distribution of loop length l in both regimes l similar to 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 lambda=l/N as lambda -->1.