On the Peierls transition in exactly soluble models

We propose two simplified models in order to discuss the origin of the Peierls transition in one-dimensional systems. For the finite-mode model we show that the thermodynamic properties are described correctly by the most general mean field approximation. But the discussion of the zero-bandwidth model suggests that this result is probably due to the fact of taking into account only a finite number of phonon modes even in the thermodynamic limit.