Numerical study of the disordered Poland-Scheraga model of DNA denaturation

We numerically study the binary disordered Poland-Scheraga model of DNA denaturation, in the regime where the pure model displays a first-order transition ( loop exponent c = 2.15 > 2). We use a Fixman-Freire scheme for the entropy of loops and consider chain length up to N = 4 x 10(5), with averages over 104 samples. We present in parallel the results of various observables for two boundary conditions, namely bound-bound (bb) and bound-unbound (bu), because they present very different finite-size behaviours, both in the pure case and in the disordered case. Our main conclusion is that the transition remains first order in the disordered case: in the ( bu) case, the disorder averaged energy and contact densities present crossings for different values of N without rescaling. In addition, we obtain that these disorder averaged observables do not satisfy finite-size scaling, as a consequence of strong sample to sample fluctuations of the pseudo-critical temperature. For a given sample, we propose a procedure to identify its pseudo-critical temperature, and show that this sample then obeys first order transition finite-size scaling behaviour. Finally, we obtain that the disorder averaged critical loop distribution is still governed by P(l) similar to 1/l(c) in the regime l << N, as in the pure case.