Equilibrium properties and the phase transition of the two-dimensional coulomb gas

We consider the two-dimensional Coulomb gas. To avoid the well-known collapse of the system below a certain temperature the Coulomb interaction is cut inside a core radius. In our statistical mechanical treatment we are able to formally describe the idea that oppositly charged ions tend to dimerize to form neutral dipolar pairs. Our calculations put on a more fundamental statistical mechanical basis essentially confirm the conclusion reached by others that at some temperature the system undergoes a phase transition. Below this transition temperature the ions are unable to shield each other, and they all may be considered as bound in neutral dipolar pairs.