Malomug M. Equation of state for the two-dimensional Coulomb gas

The thesis is devoted to the investigation of thermodynamic and electro-physic properties of the two-dimensional Coulomb gas, in the first place, its equation of state and dielectric-conduction transition. It is taken into account, that anions and cations tend to joint to quadrupole clusters and multimers of higher order. The distribution of dipole pairs and quadrupole clusters in the density-temperature plan is studied with the help of the chemical equilibrium equation. It is shown, that the vapor-liquid coexistence curve is situated in the region which correspond to dilute solution of dipole pairs in a system of quadrupole clusters. The binodal and spinodal of the two-dimensional Coulomb gas are constructed in the hard dipole pairs and quadrupole clusters approximation. The thermal excitations of quadrupole clusters are investigated. It is shown that the destruction temperature for the quadrupole clusters because of the excitation of their vibration modes for extremely rare Coulomb gas is practicallycoinciding with the Kosterlits-Touwless temperature for the dielectric-conductor transition. The density dependence of the dissociation temperature for quadrupole clusters, caused by electrostatic interaction between them, is studied. It is shown that the dissociation of quadrupole clusters is accompanied by the appearance of the conductivity. Constructed within such representations the dielectric-conductor line transition is in satisfactory agreement with the results of computer experiments.