A TESTBENCH FOR THE NESTED DIPOLE HYPOTHESIS OF KOSTERLITZ AND THOULESS

We consider the two-dimensional one-component plasma without a backgro und and confined to a half-plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wa ll with an inverse-power-law Boltzmann factor. The model has a known s olvable isotherm which exhibits a Kosterlitz-Thouless-type transition from a conductive to an insulator phase as the power law is varied. Th is allows predictions of theoretical methods of analyzing the Kosterli tz-Thouless transition to be compared with the exact solution. In part icular, we calculate the asymptotic density profile by resumming its l ow-fugacity expansion near the zero-density critical coupling in the i nsulator phase, and solving a mean-field equation deduced from the fir st BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesi s of Kosterlitz and Thouless, the validity of this hypothesis is expli citly verified.