Classical-statistical mechanics of kink-bearing deformable systems: Continuum study and lattice discreteness corrections

The thermodynamical behaviour of nonlinear systems capable to support a large class of kink excitations and several kind of extended modes, as well as localized ones, is discussed in the continuum and discrete limits and at low temperatures. The substrate potentials are two deformable nonlinear double-well potentials whose shapes vary in several different manners as a function of a parameter. In the continuum limit, a few thermodynamic functions are derived for each of the two models, and shown to vary differently with the deformability parameter. We have also estimated first-order lattice discreteness corrections to some of these thermodynamic functions.