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A bstract Generalizing the quantum sine-Gordon and sausage models, we construct exact S -matrices for higher spin representations with quantum Uₐ (su₂) U q su 2 symmetry, which satisfy unitarity, crossing-symmetry and the Yang-Baxter equations with minimality assumption, i. e. without any unnecessary CDD factor. The deformation parameter q is related to a coupling constant. Based on these S -matrices, we derive the thermodynamic Bethe ansatz equations for q a root of unity in terms of a universal kernel where the nodes are connected by graphs of non-Dynkin type. We solve these equations numerically to find out Hagedorn-like singularity in the free energies at some critical scales and find a universality in the critical exponents, all near 0. 5 for different values of the spin and the coupling constant.
Ahn et al. (Mon,) studied this question.