 
Summary: Nuclear Physics B 601 [FS] (2001) 539568
www.elsevier.nl/locate/npe
Excited TBA equations I:
Massive tricritical Ising model
Paul A. Pearce a, Leung Chim a,1, Changrim Ahn b
a Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3052, Australia
b Department of Physics Ewha Womans University, Seoul 120750, South Korea
Received 29 December 2000; accepted 27 February 2001
Abstract
We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator 1,3 in a
cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that
are natural offcritical perturbations of known conformal boundary conditions. We derive massive
thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum
scaling limit, the TBA functional equation satisfied by the doublerow transfer matrices of the A4
lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of
excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point.
Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because
the classification of states is simply related to fermionic representations of single Virasoro characters
r,s(q). We study the TBA equations analytically and numerically to determine the conformal UV
and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and
