Correlations in twocomponent loggas systems
Abstract
A systematic study of the properties of particle and charge correlation functions in the twodimensional Coulomb gas confined to a onedimensional 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 zerodensity KosterlitzThoulesstype transition as the dimensionless coupling Γ:= q ^{2}/ kT is varied through Γ=2. In the chargeordered system we use a perturbation technique to establish an O(1/ r ^{4}) decay of the twobody correlations in the hightemperature limit. For Γ→2^{+}, the lowfugacity expansion of the asymptotic chargecharge correlation can be resummed to all orders in the fugacity. The resummation leads to the Kosterlitz renormalization equations. In the system without charge ordering the twobody correlations exhibit an O(1/ r ^{2}) decay in the hightemperature limit, with a universal amplitude for the chargecharge correlation which is associated with the state being conductive. Lowfugacity expansions establish an O(1/ r ^{Γ}) decay of the twobody correlations for 2<Γ<4 and an O(1/ r ^{4}) decay for Γ>4. For both systems we derive sum rules which relate the longwavelength behaviour of the Fourier transform of the charge correlations to the dipole carried by the screening cloud surrounding two opposite internal charges. These sum rules are checked for specific solvable models. Our predictions for the KosterlitzThouless transition and the largedistance behavior of the correlations should be valid at low densities. At higher densities, both systems might undergo a firstorder liquidgas transition analogous to the twodimensional case.
 Publication:

Journal of Statistical Physics
 Pub Date:
 November 1995
 DOI:
 10.1007/BF02179249
 arXiv:
 arXiv:condmat/9505015
 Bibcode:
 1995JSP....81..579A
 Keywords:

 KosterlitzThouless transition;
 loggas systems;
 correlations;
 fugacity expansions;
 sum rules;
 Condensed Matter
 EPrint:
 39 pages, 5 figures not included, Latex, to appear J. Stat. Phys. Shortened version of abstract below