Thermodynamic Bethe ansatz of the homogeneous sine-Gordon models

We apply the thermodynamic Bethe ansatz to investigate the high energy beha viour of a class of scattering matrices which have recently been proposed t o describe the Homogeneous sine-Gordon models related to simply laced Lie a lgebras. A characteristic feature is that some elements of the suggested S- matrices are not parity invariant and contain resonance shifts which allow for the formation of unstable bound states. From the Lagrangian point of vi ew these models may be viewed as integrable perturbations of WZNW-coset mod els and in our analysis we recover indeed in the deep ultraviolet regime th e effective central charge related to these cosets, supporting therefore th e S-matrix proposal. For the SU(3)(k)-model we present a detailed numerical analysis of the scaling function which exhibits the well known staircase p attern for theories involving resonance parameters, indicating the energy s cales of stable and unstable particles. We demonstrate that, as a consequen ce of the interplay between the mass scale and the resonance parameter, the ultraviolet limit of the MSG-model may be viewed alternatively as a massle ss ultraviolet-infrared flow between different conformal cosets. For k = 2 we recover as a subsystem the flow between the tricritical Ising and the Is ing model. (C) 2000 Elsevier Science B.V. All rights reserved.