The 2D Coulomb gas on a 1D lattice

The statistical mechanics of a two-dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact sel f-duality is shown for a version of the sine-Gordon model arising in this c ontext, thereby locating the transition temperature exactly. We present asy mptotically exact results for the correlations in the model and characteriz e the low- and high-temperature phases. Numerical simulations provide suppo rt to these renormalization group calculations. Connections with other inte resting problems, such as the quantum Brownian motion of a panicle in a per iodic potential and impurity problems, are pointed out.