A special case of the 20-vertex model on a triangular lattice is solved exactly for all temperatures by the method of Bethe ansatz. The model exhibits no phase transition.
The simple Bethe Ansatz is illustrated step by step in great detail for a variety of many-body quantum problems and lattice models. The focus is on a constructive presentation in which the problems of determining the spectral conditions and full wave functions are completely and transparently solved for the cases of the isotropic Heisenberg chain, N bosons or spin ħ/2 fermions with δ-function interactions, the XX-Heisenberg chain, and the six-vertex model. PACS Nos.: 05.50.+q, 05.30.Fk, 03.65.Fd, 75.10.Hk, 71.10.Fd