Phase Transition in the Peierls Model for Polyacetylene

We consider the Peierls model for closed polyactetylene chains with an even number of carbon atoms as well as infinite chains, in the presence of temperature. We prove the existence of a critical temperature below which the chain is dimerized and above which it is 1-periodic. The chain behaves like an insulator below the critical temperature and like a metal above it. We characterize the critical temperature in the thermodynamic limit model and prove that it is exponentially small in the rigidity of the chain. We study the phase transition around this critical temperature.