THERMODYNAMICS OF TODA LATTICE MODELS - APPLICATION TO DNA

Our generalised Bethe ansatz method is used to formulate the statistic al mechanics of the classical Toda lattice in terms of a set of couple d integral equations expressed in terms of appropriate action-angle va riables. The phase space as coordinatised by these action-angle variab les is constrained; and both the soliton number density and the solito n contribution to the free energy density can be shown to decouple fro m the phonon degrees of freedom and to depend only on soliton-soliton interactions. This makes it possible to evaluate the temperature depen dence of the soliton number density which, to leading order, is found to be proportional to T1/3.