  Many thermodynamic instabilities in one dimension (e.g. DNA thermal
denaturation, wetting of interfaces) can be described in terms of simple models
involving harmonic coupling between nearest neighbors and an asymmetric on-site
potential with a repulsive core, a stable minimum and a flat top. The paper
deals with the case of the Morse on-site potential, which can be treated
exactly in the continuum limit. Analytical expressions for correlation
functions are derived; they are shown to obey scaling; numerical
transfer-integral values obtained for a discrete version of the model exhibit
the same critical behavior. Furthermore, it is shown in detail that the onset
of the transition can be characterized by an entropic stabilization of an
-otherwise unstable-, nonlinear field configuration, a soliton-like domain wall
(DW) with macroscopic energy content. The statistical mechanics of the DW
provides an exact estimate of the critical temperature for a wide range of the
discretization parameter; this suggests that the transition can be accurately
viewed as being "driven" by a nonlinear entity.
