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.

24 pages

References in corpus (6)

• The large deviation approach to statistical mechanics
• Random transverse-field Ising chain with long-range interactions
• Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents
• Critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices
• Long-range epidemic spreading in a random environment
• On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder

Cited by in corpus (2)

• Results and conjectures on a toy model of depinning
• The sustainability probability for the critical Derrida-Retaux model