Phase Transition in the Peierls Model and the Possibility of One-Dimensional Melting

In 1940 Peierls proposed a model for dislocations arising as a compromise between long-range elastic forces and lattice periodicity. It implies that dislocation pairs interact with a logarithmic potential. We show that the corresponding one-dimensional statistical mechanics model exhibits a physically realizable dislocation-mediated melting transition of infinite order.