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We study the spectrum, the massless S-matrices and the ground-state energy ofthe flows between successive minimal models of conformal field theory, andwithin the sine-Gordon model with imaginary coefficient of the cosine term(related to the minimal models by ``truncation''). For the minimal models, wefind exact S-matrices which describe the scattering of massless kinks, and showusing the thermodynamic Bethe ansatz that the resulting non-perturbativec-function (defined by the Casimir energy on a cylinder) flows appropriatelybetween the two theories, as conjectured earlier. For the non-unitarysine-Gordon model, we find unusual behavior. For the range of couplings we canstudy analytically, the natural S-matrix deduced from the minimal one by``undoing'' the quantum-group truncation does not reproduce the properc-function with the TBA. It does, however, describe the correct properties ofthe model in a magnetic field.Comment: 34 pages, BUHEP-93-6, USC-93-004, LPM-93-0

MASSLESS FLOWS II: THE EXACT S-MATRIX APPROACH