  We study the scaling limits of the L-state Restricted Solid-on-Solid (RSOS)
lattice models and their fusion hierarchies in the off-critical regimes.
Starting with the elliptic functional equations of Klumper and Pearce, we
derive the Thermodynamic Bethe Ansatz (TBA) equations of Zamolodchikov.
Although this systematic approach, in principle, allows TBA equations to be
derived for all the excited states we restrict our attention here to the
largest eigenvalue or groundstate in Regimes III and IV. In Regime III the TBA
equations are massive while in Regime IV there is massless scattering
describing the renormalization group flow between distinct A_1^{(1)} coset
conformal field theories. Regimes I and II, pertaining to Z_{L-1} parafermions,
will be treated in a subsequent paper.

High Energy Physics - Theory