JANCOS DISCIPLES IN COULOMBLAND .1. THE 2D CLASSICAL COULOMB GAS NEARTHE ZERO-DENSITY KOSTERLITZ-THOULESS CRITICAL-POINT - CORRELATIONS AND CRITICAL LINE

The 2D classical Coulomb gas undergoes the famous Kosterlitz-Thouless (KT) transition between a high-temperature conducting phase and a low- temperature insulating phase. We present various studies of the correl ations in the insulating phase near the zero-density critical point. F irst, we briefly recall the phenomenological approach of Kosterlitz an d Thouless. This theory predicts that the decay of the charge correlat ion is entirely controlled by the bare Coulomb potential between oppos ite charges only renormalized by the dielectric constant epsilon. Then , we present an analysis of the low-fugacity expansions of the correla tions. The particle correlations are found to decay as 1/r(4). The lar ge-distance decay of the charge correlation is shown to be tightly rel ated to the behavior of 1 epsilon in the regime of interest. Systemati c resummations allow one to recover the algebraic decay predicted by t he heuristic KT model. This settles on a rigorous basis various assump tions of this model. In particular, the nested pair mechanism naturall y arises in the resummation scheme. Finally, we describe the phase dia gram of the system according to the most recent calculations which inc lude finite-density effects.