Scaling limit of RSOS lattice models and TBA equations. (English) Zbl 0949.82009
Summary: We study the scaling limits of the L-state restricted solid-on-solid (RSOS) lattice models and their fusion hierarchies in the off-critical regimes. Starting with the elliptic functional equations of Klümper and Pearce, we derive the thermodynamic Bethe ansatz (TBA) equations of Zamolodchikov. Although this systematic approach, in principle, allows TBA equations to be derived for all the excited states we restrict our attention here to the largest eigenvalue or ground state in regimes III and IV. In regime III the TBA equations are massive while in regime IV there is massless scattering describing the renormalization group flow between distinct \(A_1^{(1)}\) coset conformal field theories. Regimes I and II, pertaining to \(\mathbb{Z}_{\mathbb{L}-1}\) parafermions, will be treated in a subsequent paper.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 81T27 | Continuum limits in quantum field theory |
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