Correlations in the Kosterlitz-Thouless phase of the two-dimensional Coulomb gas

The particle and charge correlations of the two-dimensional Coulomb gas are studied in the dielectric phase. A term-by-term analysis of the low-fugacity expansions suggests that the large-distance behaviors of the particle correlations are governed by multipolar interactions, similar to what happens in a system of permanent dipoles. These behaviors are compatible with the asymptotic structure of the BGY hierarchy equations; on the other hand, a new identity for the dielectric constant var-epsilon is used to show that the four-particle correlations decay as the dipole-dipole potential 1/r2 when two neutral pairs are separated by a large distance r. Near the zero-density critical point of the Kosterlitz-Thouless transition, the authors resume the low-fugacity expansions of both 1/var-epsilon and the charge correlation C(r). Thus the coupling constant flow equations of the renormalization group are retrieved as well as the effective interaction energy of the iterated mean-field theory by Kosterlitz and Thouless. The coupling constant at the RG fixed point is then identified with a/var-epsilon. The nonanalyticity of 1/var-epsilon at the transition turns out to coincide with the divergence of the low-fugacity series for this quantity. The leading term in the large-distance behavior of C(r) is found to be the same as for external charges. Moreover, the subleading terms are exhibited with also contribute to 1/var-epsilon