DNA melting: A phase transition in one dimension

We show that a one-dimensional system of particles coupled by nearest-neighbor anharmonic interactions and subjected to an on-site Morse potential, corresponding to a model originally developed for DNA melting, exhibits a first-order phase transition. This result is obtained by an exact treatment of the transfer integral operator, using two independent methods. It is confirmed by molecular dynamics simulations. We discuss the conditions that a one-dimensional system of particle with short-range interactions must fulfill to exhibit such a first-order transition.