Exact and Asymptotic Solutions for Bethe Ansatz in a Hexagon

Abstract

A complete set of solutions of the Heisenberg model for a magnet with N=6 nodes and spin s=1/2 has been described in terms of (i) immediate diagonalization, (ii) coordinate Bethe Ansatz (in terms of pseudomomenta pα and soliton phase exchange Ф α,α′), (iii) algebraic Bethe Ansatz (in terms of spectral parameters λα), (iv) string hypothesis with its combinatorial content (rigged configurations of Kerov-Kirillov-Reshetikhin). It has been shown that this example transparently presents various notions and terminology associated with Bethe Ansatz, and, in particular, indicates distinction between exact and asymptotic solutions.