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

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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 · 10⁵, 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 behaviors, 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 behavior. Finally, we obtain that the disorder averaged critical loop distribution is still governed by P(l) 1/lᶜ in the regime l ≪ N, as in the pure case.