Order of the phase transition in models of DNA thermal denaturation

We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically: depending an the stiffness parameter, it is shown to have either ii) a second-order transition with nu(perpendicular to) = -beta = 1. nu(parallel to) = gamma/2 = 1 (characteristic of short-range attractive part of the Morse potential) or iii) a first-order transition with finite malting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents nu(perpendicular to) = -beta = 1/2, nu(parallel to) = gamma/2 = 1.