Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-07-16
J. Stat. Phys. 106 (2002) 857-874
Physics
Condensed Matter
Statistical Mechanics
18 pages, 3 figures
Scientific paper
The model under consideration is the two-dimensional Coulomb gas of $\pm$ charged hard disks with diameter $\sigma$. 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 $0 \le \beta < 2$, where its full thermodynamics was obtained exactly [L. {\v{S}}amaj and I. Trav{\v{e}}nec, {\it J. Stat. Phys.} {\bf 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 $\sigma$ (appearing in the dimensionless combination $n\sigma^2$, $n$ is the particle density). This permits us to extend the treatment to the interval $2\le \beta <3$ (the Kosterlitz-Thouless phase transition takes place at $\beta=4$). The results, which are exact in the low-density limit $n\sigma^2 \to 0$, reproduce correctly the singularities of thermodynamic quantities at the collapse point $\beta=2$ and agree very well with Monte-Carlo simulations.
Kalinay Pavol
Samaj Ladislav
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