Exact Solution for the One-D Spin Fluctuation Model

The exact solutions via Bethe ansatz to the One-D spin fluctuation model for J ＞0 and J ＜0 are presented . The bound states are discussed based on the Bethe ansatz equations. It is shown that the antiferromagnetic spin fluctuation leads to bound states like Cooper pairs and ferromagnetic spin fluctuation to no bound state. Also we point out that our model is much similar to the δ–potential Fermi gas model.