Thermodynamic Properties of the Two-Dimensional Coulomb Gas in the Low-Density Limit

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The model under consideration is the two-dimensional Coulomb gas of ± charged hard disks with diameter σ. For the case of pointlike charges (σ=0), the system is stable against collapse of positive-negative pairs of charges in the range of inverse temperatures 0 ≤ β< 2, where its full thermodynamics was obtained exactly [L. Šamaj and I. Travěnec, J. Stat. Phys. 101:713 (2000)]. In the present work, we derive the leading correction to the exact thermodynamics of pointlike charges due to the presence of the hard core σ (appearing in the dimensionless combination nσ², n is the particle density). This permits us to extend the treatment to the interval 2≤ β<3 (the Kosterlitz-Thouless phase transition takes place at β=4). The results, which are exact in the low-density limit nσ² → 0, reproduce correctly the singularities of thermodynamic quantities at the collapse point β=2 and agree very well with Monte-Carlo simulations.