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 on the stiffness parameter, it is shown to have either (i) a second-order transition with ${\nu }_{\perp }=-\beta =1,{\nu }_{||}=\gamma /2=2$ (characteristic of short-range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents ${\nu }_{\perp }=-\beta =1\mathrm{}/2,{\nu }_{||}=\gamma /2=1$.