Numerical study of DNA denaturation with self-avoidance: pseudo-critical temperatures and finite size behaviour

Abstract

We perform an extensive numerical study of the disordered Poland-Scheraga (PS) model for DNA denaturation in which self-avoidance is completely taken into account. In complement to our previous work, we focus here on the finite size scaling in terms of pseudo-critical temperatures. We find notably that the mean value and the fluctuations of the pseudo-$T_c$ scale with the same exponent, the correlation length exponent ${\nu }_r$ (for which we provide the refined evaluation ${\nu }_r=2.9\pm 0.4$). This result (coherent with the typical picture that describes random ferromagnets, when disorder is relevant) is at variance with numerical results reported in the literature for the PS model with self-avoidance, leading to an alternative scenario with a pseudo first order transition. We moreover introduce a crossover chain length $N^{\ast }$, which we evaluate, appropriate for characterizing the approach to the asymptotic regime in this model. Essentially, below $N^{\ast }$, the behaviour of the model in our study could also agree with such alternative scenario. Based on an approximate prediction of the dependence of $N^{\ast }$ on the parameters of the model, we show that following the choice of such parameters it could be not possible to reach the asymptotic regime in practice. In such context it becomes then possible to reconcile the apparently contradictory numerical studies.

arXiv comment31 pages with 20 ps figures. Revised version with major improvements in the presentation of the results and some references added. This is the manuscript version that has been accepted for publication

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Cited by in corpus (2)

• Strong Disorder Renewal Approach to DNA denaturation and wetting : typical and large deviation properties of the free energy
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates