Numerical study of a disordered model for DNA denaturation transition

We numerically study a disordered version of the model for DNA denaturation transition consisting of two interacting self-avoiding walks in three dimensions, which undergoes a first order transition in the homogeneous case. The two possible values (epsilon) over cap (AT) and (epsilon) over cap (GC) of the interactions between base pairs are taken as quenched random variables distributed with equal probability along the chain. We measure quantities averaged over disorder such as the energy density, the specific heat, and the probability distribution of the loop lengths. When applying the scaling laws used in the homogeneous case we find that the transition seems to be smoother in the presence of disorder, in agreement with general theoretical arguments, although we cannot rule out the possibility of a first order transition.