From asymptotic to finite Heisenberg chain - the evolution of Bethe solutions

Solutions of Bethe equations are found for different numbers of nodes in the Heisenberg chain for S = 1/2 and for chosen winding numbers. The computing procedure starts from asymptotic solutions. It is shown that the evolution of solutions has quasi-continuous form even for a wide range of nodes number N. However, it is observed that in some cases critical and limiting points appear.