Collective behaviour of a two-dimensional array of interacting lines

A statistical two-dimensional interacting line model is defined in terms of three parameters describing the line stiffness, the line-line interaction and an external restoring force. It describes the collective properties of various physical systems like reconstructing surfaces, disordering stepped surfaces and adsorbed interacting polymers. The statistical properties are calculated by a Monte-Carlo method. The resulting phase diagram is presented for various parameters and an Ising critical behaviour at the phase boundaries is established. For the case of competing interactions a disorder line is found.