THERMODYNAMICS OF TODA LATTICE MODELS - APPLICATION TO DNA

Our generalised Bethe ansatz method is used to formulate the statistical mechanics of the classical Toda lattice in terms of a set of coupled integral equations expressed in terms of appropriate action-angle variables. The phase space as coordinatised by these action-angle variables is constrained; and both the soliton number density and the soliton contribution to the free energy density can be shown to decouple from the phonon degrees of freedom and to depend only on soliton-soliton interactions. This makes it possible to evaluate the temperature dependence of the soliton number density which, to leading order, is found to be proportional to T1/3.