Journal of Statistical Physics, Vol. 42, Nos. 5/6, 1986, p. 871-894.
The one-component Coulomb system with logarithmic potential in a periodic background is considered. In one dimension, when the background has the same period as the average interparticle spacing, the system is exactly solvable for three values of the coupling constant. The exact solution exhibits insulatingconducting phase transitions. An heuristic argument is presented which predicts the phase diagram for this system.