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

TL;DR

This numerical study investigates the disordered Poland-Scheraga model of DNA denaturation, demonstrating that the first order transition persists despite disorder, with significant sample-to-sample fluctuations affecting finite-size scaling.

Contribution

The paper provides the first detailed numerical analysis showing the first order nature of the transition remains in the disordered model and introduces a method to identify pseudo-critical temperatures for individual samples.

Findings

Transition remains first order with disorder.

Disorder averaged observables do not follow finite size scaling.

Sample-specific pseudo-critical temperatures obey first order scaling.

Abstract

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 $N=4 \cdot 10^5$, with averages over $10^4$ 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 $P(l) \sim 1/l^c$ in the regime $l \ll N$, as in the pure case.