Strong Disorder Renewal Approach to DNA denaturation and wetting : typical and large deviation properties of the free energy

24 pagesInternational audienceFor 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 $\ln \xi(T) \propto |T-T_c |^{-1}$. In the critical region, we analyze the statistics over samples of the free-energy density $f_L$ 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 $\overline{Z_L^q} $ 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