CORRELATIONS IN 2-COMPONENT LOG-GAS SYSTEMS

A systematic study of the properties of particle and charge correlatio n functions in the two-dimensional Coulomb gas confined to a one-dimen sional domain is undertaken. Two versions of this system are considere d: one in which the positive and negative charges are constrained to a lternate in sign along the line, and the other where there is no charg e ordering constraint. Both systems undergo a zero-density Kosterlitz- Thouless-type transition as the dimensionless coupling Gamma:= q(2)/kT is varied through Gamma = 2. In the charge-ordered system we use a pe rturbation technique to establish an O(1/r(4)) decay of the two-body c orrelations in the high-temperature limit. For Gamma --> 2(+), the low -fugacity expansion of the asymptotic charge-charge correlation can be resummed to all orders in the fugacity. The resummation leads to the Kosterlitz renormalization equations In the system without charge orde ring the two-body correlations exhibit an O(1/r(2)) decay in the high- temperature limit, with a universal amplitude for the charge-charge co rrelation which is associated with the state being conductive. Low-fug acity expansions establish an O(1/r(Gamma)) decay of the two-body corr elations for 2 < Gamma < 4 and an O(1/r(4)) decay for Gamma > 4. For b oth systems we derive sum rules which relate the long-wavelength behav iour of the Fourier transform of the charge correlations to the dipole carried by the screening cloud surrounding two opposite internal char ges. These sum rules are checked for specific solvable models. Our pre dictions For the Kosterlitz-Thouless transition and the large-distance behavior of the correlations should be valid at low densities. At hig her densities, both systems might undergo a first-order liquid-gas tra nsition analogous to the two-dimensional case.