Thermodynamic properties of the two-dimensional Coulomb gas in the low-density limit

The model under consideration is the two-dimensional Coulomb gas of charged hard disks with diameter a. For the case of pointlike charges (sigma = 0), the system is stable against collapse of positive-negative pairs of charges in the range of inverse temperatures 0 less than or equal to beta <2, where its full exact thermodynamics was obtained recently. In the present work, we derive the leading correction to the exact thermodynamics of pointlike charges due to presence of the hard core sigma which enables us to extend the treatment beyond the collapse point beta = 2. Our results, which are conjectured to be exact in the low-density limit in the interval 0 less than or equal to beta < 3, reproduce correctly the singularities of thermodynamic quantities at the collapse point and agree well with Monte-Carlo simulations. The ''subtraction- mechanism within the ansatz proposed by M. E. Fisher et al. [J. Star. Phys. 79 1 (1995)], which excludes the existence of intermediate phases between the collapse point beta = 2 and the Kosterlitz Thouless transition point beta(KT) = 4, is confirmed, however, a different analytic structure of this ansatz is suggested.