Order of the phase transition in models of DNA thermal denaturation

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