Strong disorder renewal approach to DNA denaturation and wetting: typical and large deviation properties of the free energy

Abstract

For the DNA denaturation transition in the presence of random contact energies, or equivalently the disordered wetting transition, we introduce a strong disorder renewal approach to construct the optimal contacts in each disordered sample of size L. The transition is found to be of infinite order, with a correlation length diverging with the essential singularity . In the critical region, we analyze the statistics over samples of the free-energy density fL and of the contact density, which is the order parameter of the transition. At the critical point, both decay as a power-law of the length L but remain distributed, in agreement with the general phenomenon of lack of self-averaging at random critical points. We also obtain that for any real q > 0, the moment of order q of the partition function at the critical point is dominated by some exponentially rare samples displaying a finite free-energy density, i.e. by the large deviation sector of the probability distribution of the free-energy density.