Correlations in two-component log-gas systems

Abstract

A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is undertaken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a zero-density Kosterlitz-Thouless-type transition as the dimensionless coupling Γ:=q2/kT is varied through Γ=2. In the charge-ordered system we use a perturbation technique to establish an O(1/r4) decay of the two-body correlations in the high-temperature limit. For Γ→2+, the low-fugacity expansion of th..