Excited TBA equations I: Massive tricritical Ising model

We consider the massive tricritical Ising model M(4, 5) perturbed by the th ermal operator phi1,3 in a cylindrical geometry and apply integrable bounda ry conditions, labelled by the Kac labels (r, s), that are natural off-crit ical perturbations of known conformal boundary conditions, We derive massiv e thermodynamic Bethe ansatz (TBA) equations for all excitations by solving , in the continuum scaling limit, the TEA functional equation satisfied by the double-row transfer matrices of the A(4) lattice model of Andrews, Baxt er and Forrester (ABF) in Regime III. The complete classification of excita tions, in terms of (m, n) systems, is precisely the same as at the conforma l tricritical point. Our methods also apply on a torus but we first conside r (r, s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters Xr,s(q). We study the TEA equations analytically and numerically to determi ne the conformal UV and free particle IR spectra and the connecting massive flows, The TEA equations in Regime IV and massless RG flows are studied in Part II. (C) 2001 Elsevier Science B.V. All rights reserved.