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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 $\ln \xi(T) \propto |T-T_c |^{-1}$. 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.
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Submitted on : Tuesday, February 21, 2017 - 3:36:19 PM
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Cécile Monthus. Strong Disorder Renewal Approach to DNA denaturation and wetting : typical and large deviation properties of the free energy. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2017, 2017 (1), pp.13301. ⟨10.1088/1742-5468/aa53f8⟩. ⟨cea-01473107⟩

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